Grab adhesive like no more nails is totally unsuitable, it wont run into cracks. Epoxy is an excellent glue, but most formulations are too thick to run fully into the crack. You can get very thin epoxy, it woudl be ideal but you wont have it in stock.
50/50 diluted pva would run in - but you then need to clamp the thing up while it sets. That can be done by screwing into the top of the non- nose section to permit clamping. PVA wont work if an open gap is left.Another option is to trim out a ltitle wood to enable metal strips to be sunk in flush and screwed down. The result would be less stong than gluing.
NT