Since your in Atlanta - no salt - the cats should come off pretty easily with standard hand tools. THere all flanged. Pull the inner fenders, remove the heat shield, undo the bolts, undo the exhaust hangers - there are two - slide everything back and take both primary cats off full. Pull them off and have a look - shake them. they shouldn't rattlle. If anything falls out that is bad. Yes, your primary cats are likely plugged, which caused a misfire and put you in limp mode. That is the most likely scenario based on your description.
I wouldn't think about selling it. Its worth about 500 bucks in its current state to the right buyer maybe $1000.00.. I know money is tight, but at that point its all but worthless. Pull the cats, have a look, gut them if you need to, and go from there.
As for why the mechanics won't look - that's been answered. Mechanics these days are worthless, and they probably figure based on your budget that if they get them off they won't be able to fix it for you anyway - since they can't legally gut them for you - all they could do is take your money and tell you there plugged. New cats a the shop are expensive.