Good Transmission?

I have a 75 F-150 that I am building up to be a mudder.  I am putting a 393 stroker in it and 44" tires on it.  I am going to put in somewhere around 5:13 gears in the diffs and I was wondering if that would work well with the Borg Warner T-18 tranny or if those gears would put too much stress on the trans.  If so should I use different gears or a different tranny or should I just beef up the tranny I have and how would I do that?  
It takes big nuts to follow us.

You actually want at least 5.13 and better yet even deeper. A bigger concern is your axles. You need some serious axles under that truck with those tires.  

If I can find them I am probably going to go with dana 60 front and dana 60 or 70 rear with 35 spline axles plus a brace will be welded on the back of each tube for aded strength.  The axles will also be 8 lug.  I just want to make sure that the tranny won't burn up or get too stressed out and start cracking or anything like that and if it has potential to do that then is there a better tranny or is there a way to beef up the one that I have?  
It takes big nuts to follow us.

T18 is a good tranny. If you gear those axles deep enough it should workout but I would suggest a automatic is the best choice here as launches are easier for runs and you can shift up and down during run. A manual is really not best choice here.  

Would I be able to set up my truck so that the front and rear diffs have limited slip and also an air or electrical powerd locker of some sort that I can enguage and disenguage with a switch in the cab so that if I am rolling on pavement or a dirt trail I can have limited slip so things don't bind up but when I get down in the mud I can lock in the axles so I have power to all wheels but once I get out of the mud I can unlock the axles?  Is there a way I can set the truck up that way or is there a better way?  
It takes big nuts to follow us.

There is a argument to be made for a open or LSD diff rather than a locker in mud running. Even with a open diff, all wheels receive same torque, no more, no less so all wheels are "powered". With a open of LSD in mud it lets individual wheels vary in speed a bit to seek their best bite. A locker does not let this happen. On the trail of rock crawling  a locker can have more value but in the mud pit it is very debatable.