i think this some time ago as well on some really old accounts that did not have many 100;s but back then you could only do snail mail
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I've also done this before, it's fairly painless. Talking them into moving accounts didn't seem to be possible.
Without Heirlooms it's not clear that throwaway RAF is worth it. Boost Level 17.5x at 300% xp (2 final accounts at a time), versus Level 10x at 155% xp (5 accounts at a time). Equating those to no heirloom/no RAF, the boost path is as hard as 6.452 trips without RAF(or heirlooms). The leveling teams path is as hard as 5.882 trips without heirlooms(or RAF). The decision pretty much comes down to is it faster to boost to max or team level to max.
If you were willing to use transfers off the throwaway accounts, the boosting method gets a lot better as you only need to do it about 10.5 times or 3.5 no RAF/no heirloom boosts. Or you could consolidate characters you care about and delete accounts to gain RAF+heirlooms. Or invest a bit of time on the throwaway battle.net to earn heirlooms (only need 1 set).
However if those options are off the table, I think your call to team level is probably the faster option. Note that boosting probably can use a 15% guild banner which would mean it's 345% XP.
You've inspired me! I've just submitted a ticket to nuke my old boxing licences so I can replace them with new RaF accounts. I'm hoping the ticket will be processed in time for me to make use of the sale that ends later today.