You're fine, time-wise. And Théodred was in the film, so you should be able to get an avatar. The problem is that there's not all that much said about him, and his only direct appearance in the books is in
Unfinished Tales, describing the battle where he was killed... er... which now never happened...
Here's what we do know about "you"–
–You're forty-one years old.
–You're an experienced warrior and commander; in fact you're Second Marshall of the Mark (second-in-command after the King).
–You're devoted to your father, and did your best to counter Gríma Wormtongue's influence on him.
–Saruman saw you (with Éomer) as the main obstacle to his conquest of Rohan. At the first battle of the Fords of Isen, he gave special orders that you were to be killed at all costs. (Or rather, he would have done so, had this battle taken place in our version.)
–You're brave– had you, in fact, died, it would have been a very heroic death.
–You're quite likely rather suspicious of Elves.
–Until recently, you would have thought hobbits were a myth.
I hope this helps.