A syringe is definitely a possibility, doubt I've got a steady enough hand to prevent any over spill but will be a lot cleaner than my method of smearing it until it fills the gaps ha.
I have some film that's designed for CNC machining, can't for the life of me remember the name, think it begins with O. It's adhesive backed and you apply it before cutting. Wonder if this will be enough to allow me to wipe off any excess epoxy.
Might give painting a try too, saw someone mention if you use thick milk paint you don't have to seal the wood before hand to prevent seepage.