i've recently revisted tryndamere in TT and i find him absolutely amazing.
i personally like building crit first, since his damage comes from criticals. bloodlust gives added crit damage, as well as attack damage and the lower the hp the higher the critical. thus i like to stack critical until approximately 60% (including runes/masteries and such) then i'll dive into AD, with the occasional stop in ASville with last whipser.
basically i like to build zerker greaves (if ninja tabi/merc treads are not necessary) avarice blade, cloak of agi, zeal, then work towards infinity edge. once i do i'll get last whisper or build youmuu's. from there i'll go bloodthirster but when i need a slot free i'll upgrade to phantom dancer.
i like to end up with zerker greaves, youmuus ghostblade, infinity edge, phantom dancer, bloodthirster last whisper. with this your crit chance is near 100% (easily 100 at half life or so) with 2+ attack speed when ghostblade is active, and 360+ attack damage. i actually played a game earlier where i finished this build on TT (game lasted 47 minutes) and i was criting for near 1200 damage, and 2 hit teemo. attack speed is a great accessory with high attack damage and critical just because you can get 2-3 hits off before they can even walk around you.
i realize attack speed isn't the most helpful thing when your targets are always running, but it isn't always the case. plus these items all give other essential things, so i do not get only pure attack speed items. last whisper is the highest DPS item you can get, we can all agree...phantom gives great amount of critical (highest in game) and youmuu's gives more penetration plus damage/critical with a speed boost and attack speed active...so it fits very well.
you'll also VERY quickly fill up bloodthirster since you'll 1 hit every minion in the game.
i do agree trynd can be decent in the lane. you're right he won't dominate, but its easy enough to not die thus not harming your team. you will be able to last hit fine, and with a decent lane mate you'll even get a couple of kills especially if you use elixirs. i personally love elixir of agility early TT and use it almost constantly until i am working or finishing infinity edge. it just adds so much DPS with crits and attack speed and allows you to jungle if you're lane is difficult. i have a new found love for this champ