But now when I send an email to an address on that domain, Plesk treats it as local and returns an error:
Sorry. Although I'm listed as a best-preference MX or A for that host, it isn't in my control/locals file, so I don't treat it as local. (#5.4.6)
I had disabled mail in the Plesk CP thinking that that would allow it, but to no avail

Is it possible to get the domain to send the emails to the remote (current) host short of deleting all DNS records and having to then change them all again once the name servers resolve to our servers. We wanted to make the transition smooth, and it appears that this email problem is the only sticking point we have.
Many thanks in advance for any advice.
EDIT 1. I forced it by creating an MX record with higher priority (& associated A record) pointing to the current provider. But I assume that when the name server change takes effect, this will then cause emails to get lost until we remove those entries, would it not??