Lets think about why Tryndamere players feel like they have to split push all game.

All he has going for him is his auto attack damage-- he is strictly inferior to Yi or fiora at assassinating squishies reliably in a complicated team fight. What I mean is that if he can't scare the bejesus out of everyone on the enemy team then they can just put a disruptive tank on top of Tryndamere and prevent him from doing anything in a team fight. Even if they don't have that they can still zone him off with slow fields and knock backs because Tryndamere isn't particularly fast and spinning slash isn't a particularly quick dash. At the end of the day its just plain hard to fight with Tryndamere in a team fight without being focused and denied the ability to contribute anything meaningful, so this is exactly why most Tryndamere players just split push.

When he doesn't have anything particularly valuable to offer in a team fight he ends up being relegated to split pushing all day. There are plenty of champions that can split push every bit as well as Tryndamere, including Jax, Nasus, and Yi. The difference is that those champions don't HAVE to ALWAYS split push because they have something valuable to offer in a team fight. Tryndamere simply put, doesn't do enough damage to the people who want to sit on him in a team fight to keep him from trying to 2 shot a squishy. Jax has magic damage and enough durability to ignore the base damages that tanks have, and Yi has true damage and his attack speed cannot be slowed by wardens mail or frozen heart. Fiora is just impossible to peel outside of killing her inside the duration of a stun.

I'm not saying Tryndamere is bad at split pushing or that he is a weak champion. In fact he is overall quite strong. I'm saying that he doesn't have options. He just does the same thing every game because he doesn't have any real choice in the matter, and its boring to play against and its quite boring to play with.

The whole reason RIOT keeps Tryndamere weak as a team fighter is because they don't want someone who can be immune to death 2 shotting squishies with no counterplay-- they want to ensure that there is always a way to prevent Tryndamere from killing your carry no matter what your team comp is, because if you feel as though you can't then Tryndamere becomes what he was before his rework in season 2, a low counterplay hard carry.

I propose to fix that by making it impossible for Tryndamere to 2 shot anything-- he might need as many as 4 hits at the bare minimum to kill the squishiest of targets now, and likely 5 or 6.

Tryndamere should do 1*AD true damage on a crit instead of 2*AD physical damage like everyone else.

The strength he gets as a tradeoff for this and the other weaknesses mentioned above is that he would kill virtually anyone in 4 seconds. Consider that most squishies will have 2000ish hitpoints and an end game flat armor pen based Tryndamere can kill a squishy in 2 hits, which takes about 1 second. With this proposed change he would need 4 hits at the least because he would do at most half as much damage per second against a squishy with less than 100 armor, so he would need a bit more than 2 seconds. Most tanks have a combination of armor and health, and usually not more than 4000 health; but 4000 is only twice 2000, so it would only take Tryndamere roughly 4 seconds to kill a tank since he pretty much ignores armor after getting some critical strike chance from items.

I just think Tryndamere should be able to kill anything in less than 4 seconds, and nothing in less than 2 seconds. If you are standing near Tryndamere in a team fight, it doesn't matter if you are malphite or rammus with 500 armor-- he should punish you hard, and the reason that is fair is because he doesn't last forever. It isn't hard to force Tryndamere to activate his "time limit" and after 5 seconds he becomes a worthless liability in a team fight. So before and during that 5 seconds he ought to damn well be able to throw his weight around no matter which tanky bruiser is trying to push him around.

The basic idea is to make him less of an assassin and more of a fighter. He wouldn't really care who he is hitting since he does the same damage number to everyone, he just cares that he is actually hitting something. That makes him more flexible in team fights since you can zone off tanks like nautilus and maoki, UNLESS you are focused with CC. This change doesn't make Tryndamere any less susceptible to CC than he is now, but it offers him a way to be strong without mandating that he dive the enemy carry each and every time with no choice involved.

It also makes him a bit easier to handle in a split push because his damage is roughly half as much as it currently is against squishy targets late game. That means it becomes much easier for someone like lissandra or lucian to burst Tryndamere and survive him for long enough for his ult to expire.

It does make Tryndamere incredibly strong against tanks and off tanks, but it also makes him much weaker against a variety of other champions, like mages and marksmen.