Both styles are flatbows, with different approaches to the outer limbs and tiller profiles. Both are suited for ash.
A meare heath replica would have too wide of tips.
A holmegaard replica would be better performance-wise because of the narrow tips..
But if you narrow the limb tips of a meare heath, I think you'd wind up with a holmegarrd-esque bow by default.
To me, it sounds like you're wanting to make a flatbow, but are deciding what approach you want to take with the outer limbs (narrow/stiff versus fat/slightly working).
Seems like you're leaning towards a flatbow that is 1.75"-2" for most of the meat of the limbs, tapering in the last third or so to under .5". Depending in what type of tiller profile you want will determine how close to a holmegaard in style that you want to get to. The stiffer the tips, the more holmegaard it gets. Designs can be modified to suit your needs. No need to follow one particular style unless you want a replica. I'm not much into replicas, I'm more into design. Match the design with the wood species, and your needs.