I'll echo some of the comments here, your Peavey TNT is a good, solid workhorse, but it's not an amp for getting the best out of a bass. I'd certainly look into trying some other amps, just to see.
For grins, take your bass to a shop and plug into something TOTALLY different, say, a Markbass and see what you think. You may not care for the Markbass tone (or you might love it) but then might find something that you feel differently about.
In my opinion, and not saying this applies here, but I'd always prefer a GREAT amp with an acceptable bass in preference to a STUNNING bass through an average amp.
Cheers,
James