Rain streaks on interior door plastic

[SaerinRhoe]

Hi folks,

After some recent rain where my windows were left down, I've got some minor streaking on the lower black plastic portion of both interior door panels. This is the smooth black plastic below the light gray armrests.

I've tried wiping the streaks down with a damp cloth, then I tried some cleaning wipes, then I took the car and had it washed and detailed inside. At best, the streaks disappear for a day or two but then they slowly return. I've also got some minor spotting on the dash.

Does anyone have ideas on how I can clean the panels to remove the streaking? I don't know what chemicals might be too hard or abrasive to use on the plastic and I don't want to mess up the panels.

Thanks,

S.R.