The burnt fluid is usually a very bad sign.
I imagine that being in limp mode would beat the living dog shyt out of the torque converter. It would be like slipping the clutch to get the car moving into third. Also, the clutch for 3rd gear could be pretty well destroyed by now, too.
To burn ATF something has got to be really messed up in there and the fluid got VERY hot. 300-400 degrees F.
I know when you are being especially hard on a torque converter, it creates heat. When it gets hot, the propensity for cavitation to ocour increases. Basically, its the creation and collapse of small air bubbles that cause a "sandblasting" effect on parts of the transmission (combined with particulate contamination especially) and the torque converter especially. The fins will eventually become so damaged the fluid coupling ability of the torque converter will be compromised. You can actually feel cavitation happening in the converter feels like 'driving on rumble strips' or can be felt as driveline shudder under acceleration. The crappier and more broken down the fluid the easier it is for cavitation to occur and the more particulate matter in the fluid, the more damage that cavitation can do.
Depending on how bad the burnt fluid is, I'd be impressed if the transmission works normally ever again.