Ich Treatment for Community Tank with Panda Cories

I've been battling ich in my community tank for the last few days. The only fish in my tank showing any signs are my rummy nose tetras. The rest of the inhabitants, Panda Corys, Lambchop Rasboras, and a clown pleco seem fine. Everybody is eating fine, and I switched to flakes and pellets infused with garlic.

I've been treating with Ich-X and following the instructions, (5ml per 10 gallons every 24 hours, 30% water change before each new dose), and things seemed to be trending in the right direction until today, where the number of white spots seems to have increased significantly.

I've been hesitant to raise the temp in my tank, but more and more I'm tempted to try, I just worry about the Corys. How will they hold up for two weeks at 86°F/30°C? I know it's out of their range.

My other two questions regarding Ich-X are, how important are the water changes? Are they solely to reduce the amount of meds in the water, or are they to remove the parasite as well? If I skipped the water change, would I be overdosing?

Can/should I continue the medical treatment if I raise the temp?

Thanks in advance!

Edit: Photos attached. Seems like there are fewer spots now than when I first woke up...