I hope I can make sense here...the kids are playing a quick soccer game with dad before bed.

(Our kids don't wind down...they just crash

) Anyway, there are a few balls whizzing by.
My husband was homeschooled using Abeka growing up, and my mother-in-law still uses it for my husband's youngest brother. It is a textbook approach...which you obviously would know rather than the living books which HOD uses for the history and science. (I am excited to use a living book appraoch with my kids because I didn't get to learn this way growing up.) Abeka is also a drill, memorize these facts for a test...and forget them. At least that is what I've seen happen. I agree with Charlotte Mason that when kids get to form relationships with what they're learning by really being interested and involved, they'll remember so much more.
HOD isn't built around a phonics program. (I know you mentioned that in your post.) You would be free to use whatever you want for phonics along with LHFHG or BLHFHG, HOD's reccommendations or not.
Besides being easy to "pick up and go" for the teacher, I am SO excited to keep using HOD for the meaningful learning and memories with my kids!
HTH

Kathleen