'Drift though' is viable for colour print processing in tubes/drums.

I presume it would work, but then again perhaps not as well as constant temperature. I know that colour negative film (c-41) (and reversal E-6) films are what are called integral tripacks.
There are three acive image layers (as many as 19 layers actually if I recall corectly from my first read of Shanebrook's most interesting book 'Making Kodak film).

The deepest colour layer may develop later that the top one, and if the temperature has changed at that later time, it may develop to a different end result density than that relative to the density of the top layer, which mostly finished its development perhaps before the deepest layer even got started. The msot telling test for this is to image a white to grey step wedge, and the see if there are colour shifts in the neg betweenn the white and black.

Trials with a 35mm daylight tank on drift though versus water bath could lead to clues that might hlep you scale if a solution.

Doing a few 'water runs' to evaluate the temperature issues with the larger drum.

Adding a layer of insulation to the expert drum, like the silver bubbles that are sold to beef up insulation levels on storage type hot water tanks may be a viable option in this case.