Great project! We usually play HOTT with movement in base widths; it's suggested in the book, and as you say, it makes things so much easier.
I always thought having different base depths was pretty daft. It also got me quite yelled at once by an overly competitive opponent who saw my heavy swordsmen (AdLG) as mediums and had sent the wrong matchup against them because he had forgotten that I had already notified him of the use of substitution stands at setup (which is legal).
Too much palaver for very little return in gaming. Adlg uses mostly square basing, although some are more rectangular.
Ha! Yeah, non-standard depths are permitted in HOTT and DBA too (just as well, as the HOTT hordes' depth changed between editions!).
I think there
is an aesthetic argument for the differing depths in HOTT, etc: it does give formations a different look. So blades look different from warbands, and doubled warbands look nicer when they form a square (on standard bases) rather than a column (on square bases). And doubled spears then look denser than warbands, and so on.
That said, I'm basing all my 15mm stuff on 40mm squares on the grounds that it's permissible in HOTT/DBA and essential for other things. As I've got lots of HOTT/DBA stuff in 1/72 on 60mm frontages, I'd probably double up with 80 x 40 for everything if I was going to play HOTT in 15mm (masking tape along the bottom of bases to keep elements together invisibly), to give more of a massed-battle effect with the smaller figures.