Alright, well that was slightly tricky, but I managed it without a support ticket on Fastmail:
1) Rename second account from me@lmorchard.com to lmorchard2@fastmail.com - which they allowed in settings
2) Delete alias me@lmorchard.com on second account
3) Delete the domain lmorchard.com from the second account
4) Add the domain lmorchard.com and alias me@ to my primary account
5) Triple check that my MX, CNAME, and TXT records for lmorchard.com were all correct