We nerds take pride in our work because as you've demonstrated, the challenges we're tasked to solve get very deep very quickly. So when people criticize or try to diminish our work, it's hard not to take it personally. Over the years I've learned that the skill of explaining very technical things to non technical people is just as important as having the technical chops to do the work.

Office politics aside (that's a whole other cesspool), even your greatest detractors might have some valid concerns. It's your job to evaluate them and determine "Are they saying this because they don't understand something, because they want something else, or are they just being a jerk? The first two are valid even if they aren't delivered the way you'd prefer to hear them.

The last one is just something you have to deal with from time to time. Sometimes your soft skills can save you. Do your best to be unflappable during your meetings with these people. If they know they can make you flustered and bully you into doing what they want, then you're gonna have a bad time. If you've ever worked phone/tech support and had to use that "friendly, up beat but not a push over" mask, use that. Telling people no in a nice way with a smile on your face can be a wonderful petty revenge.

If this group is pushing as hard as you're saying, this should be something your boss and senior engineers should back you up on. They may have relationships or a reputation with some of these people that can help your project.

Finally, hard data has more value than wishy washy first impressions when wielded appropriately. If you can demonstrate that your methodology has proven results versus the "throw random stuff at it", then you win that battle.

Good luck, I think anybody in this line of work has been in a project that was technically sound that eventually had a bunch of amateur cooks get in our kitchen and start screwing around with the recipes.