I just received my doors from Evans Cabinets and Doors in TX. They are wood frame with a raised MDF panel(their cheapest raised panel option). They were not primed. They look great and the turn-around time was 7 days plus shipping/transit time. Out of 35 doors and drawer front, there was only 1 small error(the hinges were drilled on the wrong side of the door-this one could not be flipped over). I will be contacting them tomorrow. Hopefully, they can send a replacement. They also have shaker style and slab doors too. Here is a link that might be useful: Evans cabinet and doors

I doubt it will stick even if you push it back with heat. If this is thermofoil cabinets Option 1 the thermofoil must be removed and re-laminated if the the MDF surface is not damaged beneath. There are companies who do re-lamination you just have to find one near you or ship the door to a near by facility you can find. If not Option 2, remove the thermofoil and paint the door with matching color which is a cheaper way out just to make a match is much harder but it can be done if the door is sprayed by a professional. Option 3, try locating your kitchen manufacturer and order a new door. Good luck

MDF is the preferred material for painted cabinets. Solid wood moves around too much, unless you have perfect in home humidity control. Then your coatings crack.

I received excellent advice from a local hardware store that was a very busy Ben Moore dealer. If you have a place like that, you should visit. From the prep, to correct primer, to best paint and applicators, comprehensive advice is the key to success. A general observation as a rookie painter is that brushstrokes look awful unless you're going for a rustic look. Talk to someone about avoiding that with the right paint, and possibly using small foam rollers, or even spraying. Supposedly, paints like BM Advance provide a better finish for cabinets, so that might work. A good paint store can make a spray can from your choice of paint (with limits). For nightstands, not much is needed and the expense might be worth it for a smooth finish.