It's true that you have to go through the Ultimate Rewards Mall to get points, but you do not have to check out with that card. I've earned over 150,000 ultimate rewards points by buying things through the Ultimate Rewards Mall and I've almost always paid with an Amex or gift card. There is a downside to this: if points don't accurately post, then you might not get help from Chase.

Regardless of that, the OP asked about using a Chase Ink card to buy Marriott gift cards for 9X. He can do this by going through the Ultimate Rewards Mall to Staples and buying Marriott gift cards there. The Ink Bold gives 5 points per dollar for office supplies (Staples does qualify), and the UR Mall gives another 4 points per dollar for Staples. So, the OP is virtually guaranteed 9X for buying gift cards.

Next, the OP can go through the UR Mall to Marriott to book the hotel. The UR Mall currently gives 3X. I'll admit that there is a small chance that he won't get the 3X when he pays with gift cards at the end of his stay, but I'd bet he will. To be safe, pay all but a few dollars with gift cards and put the rest on a Chase card.

Finally, yes, the OP will also get Marriott points for his stay. Up to 15X I believe depending on his elite status.

So, it's possible to get up to 9X + 3X + 15X = 27X points!

[Edit] Since the OP wasn't able to go through the UR Mall to register for the hotel, he will be limited to 9X UR points + up to 15X Marriott rewards. Up to 24X is still awesome!