I generally build Divisional sized transports with troop capacity of 21 or 22 Battalions, which carry either a regular division of 1x DivHQ, 4x BgdHQ and 16xBtn(pick & mix flavours) or 1x DivHQ,1xBgdHQ + 2xMI, 1xEngHQ+3xEng (the 22 cap type usually also has a Replacement Btn).
These can be loaded in the Task Groups screen (F12) by selecting the appropriate Planet, Choosing the Load Ground Unit into Transport Bay order, selecting the appropriate Division, making sure that the Load Entire Formation if HQ Selected box is checked, and then pressing the Add Move button (note there is no double click functionality in these orders).
If you're carrying out these steps and you're still not loading are you sure you have updated the ship correctly? Remember, if you have SM changed the class it doesn't affect individual ships in that class until you either do a refit or repair at a shipyard OR view the individual ship in the F6 menu
The only real problem I have at the moment is that since the Civillian vessel construction has been so badly affected in 5.52 it now takes 10 years to build each 100kt Divisional Transport whereas it used to be built at a roughly comparable rate to the 20kt naval units ie 2-3 years
