Agree with JanSz - Dr M know's what he is doing & you flew along way to see him. Let him treat you properly.
Without
test results, he may not want you on T3 (which armour also contains), until/if the results show your T3 is low. Therefore based on hypothyroid symptoms alone he may have determined T4 only is the best start - would raise your T4, and of course this converts to T3 as needed.
You may find once your
test results are back, and you have a follow up ohone consultation with him - that he may tweak or add to your protocol. You can discuss armour with him then if you are concerned.
I would think you could start them at same time, as you will be starting low on the thyroid and building up over time. I started my adrenals one day before I started my thyroid - mainly due to having to wait for the thyroid meds.
Try not to get into the loop of following/asking what everyone else is doing, as you know everyone is different & treatments vary - you are seeing one of the best, so let him decide the best way to treat you & then don't stress about it anymore.