Good morning,
From your description there are several possibilities and the torque converter is one of them. I don’t think that’s the problem, though, because it slams when you select either Drive or Reverse so I think we can rule that one out.
The next possibility is the clutch/band assembly. Normally, the clutches and bands — they work together — engage in a very defined manner. Each clutch and band assembly slips into contact with its mate (each clutch/band selection features an almost mirror image clutch/band assembly. If the clutch/band assemblies are shot then you should find that your Sebring revs a lot, but, it will be moving quite slowly because the clutch/band assembly is trying to meet its mate and fails. The result is slippage. Since your Sebring is find here, you can rule out bands/clutches
I think that the input and output shaft assembly is in good shape, though, at your car’s age now — 11 years — it’s probably a good idea to have a tech (unless you feel comfortable pulling the Sebring’s transaxle and stripping it down so you can get to the input/output shaft assemblies.
My thinking on your Sebring’s problem is this: I suspect the shift solenoids are shot. Normally, there are two solenoid packs that control your Sebring’s shifting. One is located inside the valve body while the other is external. In operation, the gearing choice for your Sebring is determined by the solenoids activated. Each solenoid pack, by the way, contains two solenoids. Drive might be all four solenoids activated for a direct linkage of all gears, while reverse may line up so that none of the solenoids engages. In any case, the transmission is thudding because the solenoids aren’t firing as they should. This is a known problem on the Sebring. You will spend roughly $350 to fix this problem, though to be honest, the price does vary with location by a few dollars. Still, the $350 figure is pretty accurate.
When you have the problem fixed be sure it is for both solenoid packs not just one. And, get the software patch that goes with this repair. Your local Fiat Chrysler Autos should help with this. If they won’t, check with a transmission specialist with the proper computerized test and repair equipment for the upgrade.