Whatever you decide, do the gum graft first. I do not think that bone recontouring is needed if it is a ‘free gingival graft’ - a small piece of tissue is removed from the palate and sutured in place over the loose tooth.
I would give it about 3 months to fully adhere to the bone before starting your infusion. FYI - I am a retired dentist whose wife has just been diagnosed with osteoporosis. Her doctor only recommended Tymlos or Forteo as they actually build healthy bone and most of the others do not.
Phil