League of Legends (LoL) Question: How To Deal With and Win Promotion Matches?

Gold 3 jungle main here. Jungling in low elo definitely can be a pain due to laners not playing safe when behind, resulting in extremely fed enemies. As Master Yi, you should have some tools to at least have a chance at winning those games. Don't try to gank losing lanes, powerfarm instead.
If you can't contest objectives, splitpushing might be the best option indeed. As Master Yi you should be able to duel pretty well, so they might have to send multiple teammembers in order to stop you. This possibly opens up opportunities for your team to contest objectives 4v3 for example.

Also if your team is too behind to fight head on, try to avoid full fights like that. Prioritize gaining gold and items and try to get picks on isolated enemies. In low elo many people will make mistakes and get caught easily. Punish those mistakes.

You probably just had some bad luck with matchingmaking during your promo's it seems. Better luck next time. Try not to worry about it, it's only a game. Have fun while playing and you'll improve while doing so.

jungle main reporting for the support group. I'm a master yi main... I mean jungle main. But seeing as how it's bronze and having been there myself and still getting some games with average bronze tiers in most of my games, it sucks, and really there's nothing you can do especially when the bot lane is hard fed because you will always lose out on drakes no matter what.

I sometimes go with all three lanes simply losing and feeding the 1v1s and 2v2s. Ganking them WILL make it worse. I usually get the first drake at level 5 when the enemy jungler goes for the second red/blue buff near the drake. You really need to pay attention to jungle camps and carry a control ward. Solo drake at level 4 or 5 and you can even get the next one or trade the second one for herald. This is before your laners have made a huge gap for your team so you still have some chances to sneak in these objectives.

In team fights if there are squishy champs you need to flank, and it's bronze so its really doable with a control ward. All you have to do is kill that one or two fed member and hope that your team can finish the job. If you are splitpushing as said in the other comment -> make sure you tell your team to not get caught or fight and after you push and the enemy teams are still pushing down your lane you can try flank onto the carries.

Also at this point I suggest you reconsider your build. You don't need to build the traditional rageblade, go for more damage the quicker you can kill the carries the better, no one is going to wait for you to stack your rageblade and deal some true damage. A carry without armor is almost true damage anyway. I personally can't remember when I actually built the jungle item - its overrated on yi against most comps in the current meta where there are not much tanks around.

And one last point - don't treat your promo as your promo until it actually matters (higher up the ranked ladder). People expect you to carry or perform without pulling their weight as negative as it sounds, it only takes a better matchmaking luck to win a few games so don't need to try hard. its not a bad thing to GG go next before you burst a vein or something.