When I joined Hilton's program a couple of years ago, I called their Rewards line and asked them to match my Marriott Rewards Plat status. They did. You might want to request Marriott Rewards to do the same. Doesn't hurt to ask these days!
Many loyalty programs have unpublished policies to do what is called "tier" matching -- meaning that with proof of your current membership in an elite tier of a program, direct competitors will often issue a trial membership in the same tier of their program. I have experienced tier matching with my loyalty cards three times in as many years (although I later dumped my Hilton Diamond due to brand dissatisfaction). You have nothing to lose by calling the Marriott Rewards office and asking for a tier match --- but be prepared if requested to send or FAX a photocopy of your current Diamond card to the MR office.