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I check-raised the flop to, as the mantra goes, to charge as much for the flush draw as possible.
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You bet and 3-bet, not check-raised.
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Now if I'm not able to manipulate the odds enough to get those draws to fold, should I back off?
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Generally, no. If you were HU with the flush draw, you would be about 2/1 on to win the hand - therefore, although the pot is big enough for the draw to have odds to call you, you make about a 1/3 profit on every dollar you put into the pot. Multiway, you're still the relative favourite to win the hand and should be putting money in on the same principle - but if there are two or more other parties calling, the flush draw will also be making money (but making it from those with top-pair-worse-kicker, middle/bottom pair, gusthots, backdoor draws, etc). Multiway you're not charging the flush draw anything - you and he are charging everybody else. I would suggest re-reading the relevant chapters of TOP.
The only strategy change to consider is in some circumstances smooth-calling the flop so that you get the chance to raise the turn if the flush card doesn't come and there's not heavy action in front of you. See HPFAP pp 170-171.