This might be a good reason to learn to shoot right-handed also. It's always good to learn to shoot with your off-hand, but I know I don't practice it as much as I should. This certainly is a good motivation, though
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But that won't help much with your M16; a lot of the gas comes straight back under the charging handle. Like others have said, there are a lot of ways to minimize that extra gas, but I've never seen a DI setup that could completely eliminate it.
If it continues to really bother you, you might want to look into the new OSS silencers. The have a wacky modular design that supposedly completely eliminates back-pressure. I don't have any personal experience with it myself, but I have a friend who tested one out on a DI AR-15 and he said it was amazing: He said it even seemed to have LESS gas-to-the-face than when shooting unsuppressed.