PLA is wrapping in overhangs

I have a major issue of PLA wrapping with parts where some overhang printing is needed. The worst case is with circle shaped holes which are located in XZ or YZ plane. The first half of circle is going well but when the circle sides are coming closer together PLA is wrapping in the edge and the printing surface is not even any more and printer will often miss some steps when nozzle hits on it during it's travelling over it. I believe wrapping is caused by thermal shrinking when pla temperature is going down. Problems started when diameter of circle is more than 15mm and this will happening even I switch cooling fan off.

Have you had problems with circle holes?
Are you using supports, will it help?
Is it common to do travel command without lifting Z-axle?
Should I use some heater instead of cooling fan in the case of circle holes?

I'm using Huxley where X and Y-axles are powered by NEMA14 motors so maybe with NEMA17 this will not be as big issue as it's now. I'm slicing my models with Cura.

PLA warping is often an issue of material quality itself, so you may want to buy some high-quality PLA and see if it helps. You also need your cooling fan to be turned on all the time with PLA.

If the material fan (blows onto the PLA) is on full (100%) try turning it down to prevent the upward shrinkage like to 50-60%

Could be over extruding also...temp too high...also make sure you are printing inside --->out verse outside / in.