Primarily AP champions whose auto attacks proc on-hit effects can effectively be build like hybrids and, in my opinion, making them the most efficient version of themselves that can exist. Their abilities are used for utility and gap-closing while their basic attacks are where they do the most work.

Less efficient than Diana but more effective in team fights, Hybrid Ekko, will be built in a way that utilizes his passive, not to push, but to kite and chase enemies. He will be extremely difficult to escape from, and will be hard to kill because of all of the life leech and mobility that his kit possesses.

This build is short since it's very easy to grasp, but take a look at it and if you like it, then try it out in a game. It promise that it will prove to be very strong if used correctly.

My choice of runes here are meant to aid Ekko with early clears and scaling just a bit more towards an auto-attacking beast. To do this, I chose to prioritize attack speed and AP as it will allow for him to trigger his passive more often. This is especially useful during his first clears because they are a bit slow and reliant on his Q for damage.

5 Marks of Attack Speed = 8.5% attack speed multiplier
4 Marks of AP = 2.4 AP
9 Seals of Armor = 9 Armor
1 Quint of Attack Speed = 4.5% attack speed multiplier
2 Quints of AP = about 9.9 AP

When added together, you will have 23 AP, 13% Attack Speed Multiplier, and 9 Armor. The 9 Armor is pretty much always needed since jungle monsters do AD and tend to hurt very early on. The mixture of AP and attack speed is something needed here because a huge problem with champions that have passives that proc every 3rd hit take too long to trigger their passives. You can give them more AP to make their abilities do more damage, but it will be decreasing their overall DPS since the time it will take to trigger their passive will not be worth the damage.

The masteries I choose for this build have proven to be quite strong for AP split pushers. They also solve some of the issue that Ekko may encounter such as clear speed, DPS, and vitality; It scales attack speed just a bit and AP quite a bit. The two masteries that I want to note on are the ones that made this build come together: Spell Weaving and Arcane Blade.
Spell Weaving improves his pushing strength, although unnoticeable earlier in the game, by a considerable amount. By stacking this mastery and then casting his Q, the damage he will do late-game is something to be reckoned with. It only increases spell damage by 3%, but when you have 600 AP things start to hit pretty hard. It's harder to execute in fights but, but is still noticeable.
Arcane Blade is the mastery that makes this build come together. I use this item on Cassiopeia because her AP, with 6 items, will pass 1,100, so the damage that she does with AA's is remarkable. That's the same principle here, except you will be able to do more on-hit magic damage because of Torment, Devourer, and Nashor's. Torment makes people more vulnerable to AP while Devourer apply the on-hit magic damage. Nashor's + Arcane Blade + Sated Devourer is 60 + 15 (+20% AP) worth in bonus on-hit magic damage. That paired with 600 AP is pretty strong.

You want to skill W first because not only will it help you with clears due to the shield an stun that it provides you with, but the bonus on-hit magic damage that it gives you when attacking enemies that are low on HP. Once you smite and throw down your W, Gromp or Krugs should be quite low aleady.

After you have W, you want to have skilled Q three times before you hit level 6 as this will be your wave clear. It speed up jungle clears by a lot once you skill it three times. You are going to want to skill E once and only once, by the latest, once you hit level 4. This allows you to maneuver from camp to camp quickly, gank, escape, or even do more damage to jungle monsters by using it with your passive.

Skill W once more when you hit level 7 just to give it more strength since the jungle monsters will be getting stronger. Once you've done this, proceed to max Q and then E leaving W for last. The reason being is that your W scales better than any other ability (besides your ultimate, of course) than any other, so you don't need to put points in it for it to be extremely effective. The cooldown is decreased, but at max rank it will still be on cooldown for two time longer than Q or E would be--and those skills are honestly a lot better for escapes and pushing. Your W's passive doesn't improve the more you skill it while your Q and E do.

I would say for you to max E first, but the damage from your Q is higher--it also provides you with a slow if you can land it correctly. You really won't even be split pushing effectively until you get your E skilled 3 times anyways.

Sated Devourer and Nashor's is needed for this build as it makes it easier for you to trigger your passive as well as making you hit harder. Ekko's passive and his E abilities grant you bonus on-hit magic damage in the form of damage procs that pile on top of the items that you build.

Sated Devourer gives you 60 on-hit magic damage along with a ridiculous passive that triggers on-hit effects twice every two AA's. This paired with the scaling on-hit magic damage that you'll be getting from Nashor's Tooth will make for quite the scary split pusher.

Ekko will also be quite the scary champion to fight because if you can't one-shot him, we will just kite and poke you down; if you can't kite him, he will just chase you down and kill you very quickly. Liandry's Torment makes for a very potent item on Ekko because almost everything he does is a slow. His passive slows, his Q slows, his W stuns, the Gunblade active slows, and all of the slows will just make the damage that Torment does very high.

I wouldn't recommend trying this build out in a Ranked match until you are at least proficient with Ekko and have tried out this build more than once. This build will fail sometimes--just like everything, but with hybrid builds, you really need to know what kind of damage you will be doing and to not rely solely on you auto attacks or your spells to kill. You need to mix them in a way that won't be wasteful. What I mean by that is you need to combo your spells correctly in order to get the most amount of damage out that you possibly can--it'll be a lot of damage, trust me.

The most efficient combo that I can think of would be to Q (it only needs to land at least one tick of your passive on them) then E into your target. Once you get your passive off, throw out your W to where you think that they'll be when it lands--your goal here is to get the stun off. When they are stunned: AA, Hydra, AA, AA, Q. By the time you Q, your W stun duration should be consumed, so use your Gunblade active on them (if they aren't dead at this point) in order to have your Torment put out the most amount of damage and keep the enemy near you.

It would be an amazing idea NOT to pick Gateskeeper Ekko if you already have a split-pusher on your team since you will be competing for farm. You can use a bruiser alternative to this build in order to be more team fight oriented and tanky without going cinderhulk; tank Ekko is a whole other thing, and I personally think that tank Ekko is ignoring lots of potential utility just to have an extra health item. But I will explore this build in another guide.

-My Final Warning-
This guide is functional, but still in the experimental stage. I have yet to figure out the different match-ups and their difficulty. I also haven't fully figured out what items are viable with this build yet due to it's hybrid nature--it's sometimes hard to find where an item will fit into a build until you've tried it out yourself. This item and skill set is the only thing that's worked exactly how I meant it to so far, but when I find out more, this guide will change accordingly.