The C & D Cases has a similar issue with engine mounting, removal of the bell housing was required and support of the engine was always an issue also, the E series and up used a SAE bell housing so removal of the TC became a piece of cake as the mounts stayed in place.
Ideally Case says to install a new cooler as well but that seldom if ever happens, However if the unit could be flushed thoroughly It would be advisable.
Bandit, yours is the typical failure, If you have access I would advise you to get one for reassembly, if read carefully it will save you much aggravation getting clutch plates lined up on the hub of the FWD clutch. If you do not have access to one get back to us and we will talk you through it, The first one of those I struggled with, reading the book the rest were easy.