Have you got any hd pictures you could share ? be good if you have . I would meet with several patients of any particular Dr you consider, and who have had a similar procedure as you are considering ( beard hair etc ) , no use meeting someone who has had 1000 grafts to there hairline if you are going for 3k beard if you know what i mean .
I think your Dr is correct with smaller procedures and proceeding slowly ,would be good if you could meet with prior patients from your Dr who have taken this route , similar graft numbers, beard, body, etc and assess there results , you need a specialist in repair with beard hair with lots of results to see
Re the rejection of another donors tissue thats quite a frightening thought , im led to believe those medicines can really make you ill , its something i would never consider
Take your time and all the best