We had a battle with these lists in the week and they worked great. Only change I made was that we gave the non livery archers longbows as well as I felt this fit the period better (even if it hurt me in gameplay terms). I would be tempted to reduce their shooting ability by one to offset that, but that may be too much.
Who do the skirmish cavalry represent? I’ve not seen any mention of cavalry behaving that way in the WotR (admittedly one never reads much about cavalry at all)