Three possible solutions, in order of preference:
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Find a different DNS provider, that will allow you to put an MX on a subdomain. Note that this does not necessarily require you to change registrars.
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Use your base domain with mailgun, perhaps utilizing their forwarding feature to send incoming mails to whoever hosts your mailboxes.
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Use someone other than mailgun, that will allow the bounce address to be set to their domain instead of yours.