Won't be cheap but most of the colocation service providers listed here, will sell you 1U-2U of rack space and DIA/IP transit for a self hosted mail server.
Don't have to connect to the SIX or have an ASN, just buy default routes from somebody with a presence near the "core" of the internet in Seattle. I'm using the SIX page there as a handy list of westin and westin-adjacent colo providers.
