Just take SQ61 from IAH to SIN and backfly SIN - India v v.

You can hypothetically make an interline connection at DME, at least to LH or LX: they're in the same terminal with SQ, and if you already have a connecting BP, you can get through security back into the departure lounge (just as the through transit passengers on SQ 61 do).

But I wouldn't recommend it without a Russian visa. And even if you do it that way, you'll end up with fairly expensive LH or LX tickets from DME to India via Europe.

Another option -- again, just get the Russian visa -- is stop over in Moscow, and buy onward tickets to DEL on SU. They fly the route daily, but they leave from SVO, not DME......