Sorry, I must have been half asleep and misread the original post and thought that the TT for trade was an alto. Grumps is correct though regarding the lacquer not being original. The horn would have originally been bare brass. Honestly, I think that your best bet would be to keep the P. Mauriat. An after market lacquer TT can be had on ebay in good shape for less than $500. Taking the original cost of the P. Mauriat into consideration, I would only trade it for a Silver or Gold plated TT in pristine condition. Please keep in mind that this is my opinion based on the current market values of the horns in question. By all means though, if the True Tone is a screamer and fits you like a glove, don't let resale get in between you and the creation of good music.
After reading your second post, I would suggest putting some money into repairing the Indiana Tenor (which by all means is a decent horn) and keep the P. Mauriat alto. This will allow you to work on both alto and tenor and that will increase your versatility when you feel that you are ready to gig. Don't feel obligated to split your playing time evenly between both horns. I spend most of my time on tenor, but still manage to squeeze in alto, soprano, clarinet, and even bass guitar.
If you feel that you have a few standards and chord progressions under your belt, by all means start looking for a local jazz club that has open stages. Professional musicians typically host these events and it is a good way to test your skills, meet some really cool musicians, and recieve free tips and lessons. I like finding as many of these open stages as possible. Actually, I've landed a few gigs this way. I will usually take a small notepad and write down any tip that is told to me. What better way to get where you want to go than by talking to people who are already there?