I was once an AP Tryndamere main, when he could be considered a serious pick, but since his heal has been nerfed he's not viable anymore. 30% of AP on his heal could be considered a nice ratio, but don't forget that the math you're doing is for an end game build, so the 250 health he gains is nothing compared to his total 2000hp at level 18. The heal does get good when you have some fury, but with an AP build with no crit it takes forever to stack, you'll be long dead before. You seem to focus on a hybrid attack speed + AP build, but all this attack speed is a bit of a waste because the damage you deal with the on-hit is nothing compared to what an AD Tryndamere can do with the same attack speed, and on top of that he'll have lifesteal to give him more sustain.
Though, AP Tryndamere is still sort of viable in URF and ARAM, with a build focus on full ap burst and cooldown reduction. When I play him I build Ionian Boots of Lucidity, Zhonya's Hourglass, Hextech Gunblade, Luden's Tempest, Lich Bane and a last AP item or a Guardian Angel.
It's a good beginng for a guide, now it's time to put your theorycrafting into practise to get to know AP Tryndamere's play style better ! Good luck !