I've never had a problem with baggage on Amtrak. Unlike airlines, most times there may be only 1 train leaving at a time, so the chance of it getting on your train is pretty good. (If you check a bag in DEN to CHI, chances are it is not going to be "accidently" be put on a train to ABQ or DAL.)
I don't know if it's possible to do what you say, but I see a problem. Amtrak will hold unclaimed checked baggage free of charge for (IIRC) 2 days. Beyond that, there is a charge. So (for instance), if you could ship a bag back, but it need to be held for 2 weeks, is it worth (I don't know the charge) $20? :huh:
And even if you could do this, and even if someone else could pick it up for you, they would not be able to retrieve it because they would not have your claim check!
Why not just have 1 bag for dirty clothes - and check that one? :huh:
IIRC, you have hours-long layovers in WAS, CHI, PDX and SAC. It may be possible (I'm not sure) to say check your (dirty clothes) bag from TPA-CHI, retrieve it in CHI and put your dirty clothes in it and then recheck it CHI-PDX, and do the same thing at each layover/connection point.
(That's assuming you would have more than a few hours between trains, considering any possible delays.)
This is what I did when I had a quick 4 day weekend trip ALB-DEN a few years back. When I boarded the LSL on Thursday night, I had 2 bags. (In fact, both were carry-on size.) I took one and checked the other. When I got to DEN on Saturday morning, I retrieved my checked bag, and then checked the other bag. When I left on Saturday night, I carried the clean bag, and the dirty bag was checked. I picked up the dirty bag in ALB on Monday morning!