As far as I know, Monzo.me transfer is technically a payment, where Monzo is the merchant, located in the UK. So unless Monzo want to get set up as a US merchant, then absorb cross border & conversion fees when they move the funds to the UK accounts (which would be relatively expensive & time consuming), unfortunately I don’t think this will be possible.
It’s also worth noting that Monzo.me may not be offered once the current accounts launch. Apart from anything else, there is a cost for processing the transactions at the moment for Monzo & obviously there will be less of a need for the service, once users can receive transfers through the Faster Payments Scheme.
However, it looks like Monzo is planning to expand into the US eventually (they’re testing dollar accounts now), at which point they might be able to solve this problem.
Also, Tom has mentioned that when the current accounts launch, Monzo will offer their first service through a partnership with an international money transfer provider (possibly TransferWise but that’s all we know for now) which may help with similar situations…