I think FLL will be fine. If your children do well with Mcguffeys, then I'd say they won't struggle with FLL. There are no frills, it is mostly done orally, but like you said the memorization are for sweet rhymes. Perfect for first grade & k. It is mastery based, so you can skip some lessons if you don't think they need them. There is enough variety, picture lessons, memorization, copywork etc. It is simple, effective and will make your LA more rounded in addition to your mcguffeys.
I've never heard of cottage press so can't offer any advice there.