You will find that it's not really about being 'authentic' more that all the best ways have already been worked out
Do not try to reinvent the wheel! Even if the old bowyers had had modern epoxy I don't think they would've used it, the reason being that virtually all hornbows need heat correction when tillering. Collogen glues can take it but you need a specific epoxy to do the same job. Sometimes areas need to be repeatedly heated and that is the killer for modern glues in this application.
There is no magic with using collogen glue you just need to learn its properties and how they can be used to your advantage. The grooving isn't hard either and doesn't need to be matching with the core grooves. The grooves filled with glue act as a 'core protector'.
As for cores......Binghams lams - no way! Grozers bows made with multiple lam cores need specialised jigs etc for glu-up. The old way is to benbd your core when still thick. This way the core acts as it's own form for horn gluing. The wood is the stiffest part of a composite and gives the bow its shape. Try gluing horn strips onto a thin core.....it isn't happening!
Again I highly recommend you follow the 'old' methods.
You need a diffuse porous wood, with medium density like maple/hornbeam/elder etc . The wood must accept glue well and be able to be steam bent into shape. If you can't find anything then contact wood mills in areas where there is a lot of maple and ask for perfectly straight grained wood, with absolutely no pin knots and ideally flatsawn. Wood is stiffest laterally in this orientation which is important in a core.
Boo will work but be careful on the node placement and good luck finding thick enough culms.