It doesn't sound like a trans problem. it sounds more like a misfire condition. This could be fuel or spark related and appears to be load related.
Separating the two is easy with some tooling. If its a fuel problem then it is probably due to the pressure dropping. If its any kind of supply problem this is how it screws with the running. The CIS system requires constant fuel pressure.
A lot can be told by looking at (and replacing) the plugs.
Bosch Master, ASE Master, L1
33 years MB technician