Let me say this first and foremost: RIOT SHOULD NOT REMOVE THE UNKILLABLE EFFECT OF UNDYING RAGE. probably an unpopular opinion but his undying rage is Tryndamere's character, it's a one of it's kind in League, and it should not be removed. Tryndamere's gimmick is to go ham for at least 5 seconds, and that should stay that way.
Besides his ult, the main problems with Trynd are: luck based early game, and tower splitting potential with ult. Here are my ideas.
Idea 1: Change his fury to giving him damage rather than crit chance. Making it so that Tryndamere's passive gives him damage removes the ability for him to triple crit you to death. Having fury give damage means there's a bit more consistency to his early game, as it's not luck whether he does more damage or not. However, a problem I see with this is that instead of having a chance to do more damage, fury will consistently give him more damage. So I say that his passive give him maybe 5% more damage at level 1, with full fury. This can increase to maybe 25% at level 16 or something. The way Tryndamere fury works currently is: 35% crit at lvl 1, increasing by 5% until he's level 16 and gets 50% crit. I'm not good with numbers so they can obviously be tinkered with, but I think that *making Tryndamere's fury give increased damage rather than crit means he's a bit more consistent to play/fight.*
Idea 2: Change his ult so that he does less structure damage while he's ulting. I play Tryndamere quite a bit, and I agree that the potential to halve or straight up destroy a tower in ult is quite bullshit, so it's simple. Change the ult, making Tryndamere to less auto damage to turrets, inhibitor, and Nexus. This change would reduce his tower destroying cheese, however I don't know the exact numbers for this. Maybe -20% damage to structures while in ult? I don't know.
Idea 3: Just reduce Tryndamere's fury gain in general. I think that the majority of late Tryndamere's fury should be his ult, because as it stands right now, Tryndamere needs a small amount of autos with static shiv, and then he's at full fury before he even ults. This might be a terrible idea but I think it's a good idea so that he's less able to delete someone without fury or ult.
feel free to downvote if my ideas are trash, or give your own opinions in the replies, etc.
edit: Had another idea. If they keep Tryndamere's passive, I think the max crit chance it should give is 25% at lvl 16. This way Tryndamere needs to build 3 crit items to get max crit, and he can't just buy two crit items (crit items being rather cheap) and then have already 90% crit chance at level 6, increasing to 95% at lvl 11.