Your mix definitely grabs my attention even though there's less groove than in the original. It seems you've got the solution to the 'less drums challenge': let the vocals carry the song fully instead of trying to compensate with other instruments. And it does sound balanced to my newbie ears. Some folks might argue about a few words at the end that could be a little too loud now:
“I want to touch the light, the heat”
But they are intentionally stressed, and if you had chosen to lower the whole track, the vocals would have lost in presence elsewhere. Personally, I prefer people who take the risk to flirt with the extremes rather than staying on the conservative side of things. So kudos to you because you dared to go for it.
Also, you asked a crucial question about the place of the vocals in the reference mix. It reminded me of what Jerry Marotta said about Peter Gabriel being a drummer himself. Sometimes, he sounds like a self-effacing singer who's drumming with his voice.
On the radio, we hear a lot of performers who have been educated with imperatives like “own the stage” and “steal the show” even though it might not serve the song. For them, In Your Eyes could be about a man who sings “I am complete”.
If the real subject is the relationship he's trying to save, then why should he occupy the forefront? The heat he's talking about is probably better personified by the percussions. But yes, as humans we relate to vocals first, so it makes mixing even harder if we don't focus on them.
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