I don’t think stuffing yourself until you feel sick is really a great solution, but I do think increasing caloric intake is important. I’ll second the advice to drink calorie dense liquids to help get there as they don’t affect the appetite much at all.
I also couldn’t eat anywhere near adequately until I realized how easy it was to drink more calories. During the last trimester of my pregnancy I was drinking almost a gallon of whole milk, with some juice, tea and water every day (totaled probably 2000+ calories just from my fluids). I still maintained very nicely concentrated urine (I do consume a lot of salt too, I’ve always liked my food salty) and I avoided the typical “pregnant lady has to pee all the time.”
In my case as long as I consumed my salt and most of the liquids were calorie dense I could drink all I wanted and my temps improved. Far more pleasant for me than over stuffing my face and feeling thirsty all the time like I was when I first started reducing my water intake.