My own approach is to have a (or several) rather large, commercial troop transports, each able to carry an entire division plus some replacement battalions. Each TT is accompanied by one or two Assault Transports, faster, heavily armored and capable of carrying a brigade.
The TTs do the moving, the ATs do the dropping
And yes, you can transfer troops from the TT to the AT in space. IIRC, the cargo handling rating of the TT is, what determines the speed of the transfer.