these juicy mechanics beyond my expertise but i would think that something is broken inside the 4.8 tranny... that may warrant opening the tranny and looking inside, to see what is broken... once you know what is broken, you may be able to cross reference parts that are broken and see if the 4.4 tranny has those parts... hoping that the 4.4 parts are still usable (due to age, mileage), pull those parts from the 4.4 and stick them to 4.8... the parts that are broken and unique to 4.8 - you would need to buy them...

it is easier said than done - for me, it is not a DIY job, i have NO IDEA how to tackle a job of this magnitude... but, if it were something else, the above approach is what i would have used to mitigate the problem with minimal expenditure...

can you do transmissions???