Unless I was misinformed or something has changed, the 5.0 manuals also use the MT-82. This being the case (and it's gonna sound weird), you gotta "sweet shift" the manual. If you try to plow through the gears, it will fight you every step of the way. Get out there and practice some rapid WOT shifting when you can, especially 4th. Once you get the feel for it, you'll understand what I mean. I used to fight 2nd through turns and 3rd and 5th all the time on the straights, but I eventually learned the "feel" of what the car "expected," and now I no longer have those issues. A new shifter, shift bracket, and maybe some other components like stiffer engine and transmission mounts should help, but for now, just get out there and acquire a better feel for what your car "wants" at WOT. I wish I could explain it more clearly, but it's something you just need to get out there and do. I recommend trying easy (but rapid) shifting followed by trying to jam it in (clutch fully engaged), to see what I mean. Only once or twice. Don't kill it, though. Wish I could be more help.
Even so, you did pretty good considering what happened on your first time out. I've seen 5.0 owners hit high 13 and low 14 second runs because of laying into it too hard with factory tires. You did alright!