Tortie peeing on clothes and fabric on floor!

Hi everyone! I have a tortie who just turned 1 year old this month. I got her at 8 weeks old and she was SO great with the litter box even after being kept outside on the porch. She wanted to use my flower pots I had inside cause of the dirt but I just hung them from the ceiling to solve that. She went into heat around 7-8 months old...I was really busy with school (college) and spay surgery always makes me nervous, she is my first unfixed cat that I have had. My oldest is was fixed when I got her. Anyway she started peeing on clothes I left on the floor when she went into heat...but it wasn't limited to just the heat period. She kept going into heat every 7-10 days so it was basically a living hell for 2 months. I got her fixed in June, and it definitely helped. But if I leave something on the floor for too long, usually my work clothes, she will pee on them. Also pees on curtains or blankets that I will have in a pile to wash in the laundry room. Honestly she for whatever reason does not have a super pungent urine so I can't even tell unless I feel it's wet or I actually check by smelling the fabric. She leaves the bedding on my bed alone, clothes in hampers, anything that isn't on the floor is safe. One detail that I am beginning to think it is an issue is that I live in a small one bedroom apartment, and the litter boxes are both in "clothing prone areas" - laundry room and bathroom. She actually almost never pees on fabric or clothes in any other room. It seems to be isolated to anything NEAR her litter boxes (there is 2 and I have 2 cats). I bought a uv light to make sure. The carpet is pee free. I had her at the vet when it started for shots and they said she was fine but I may take her again just in case. I am moving to a 2 bedroom in 5 days; my washer and dryer will be in a spare room in a closet now. There's one bathroom. I thought about placing one litter box in the spare room (it's open to the living room so it's more like an extension of the living room) but I am afraid she will take to the carpet if it's near the box since its fabric. The only rooms with linoleum is the bathroom and kitchen. I changed the litter to scent free clay. Let me make it clear, she DOES use the litter box all the time. I see her do it, not so much that it would suggest a uti but a normal amount. She has no problems using a litter box. So for those reasons I feel it's behavioral...I am hoping maybe the move will help it or it'll get worse because it's new "Territory". She's a fun cat, I love watching her play on the cat tree and she will let me hold her and love on her even if she whines, she doesn't have a mean bone in her body - just very sassy like a tortie should be! She's part of the family so I have to find a way, which the obvious idea would be to keep clothes off the floor but I am concerned that she will take to carpet in the new place.

You could try placing the litter box inside a washer pan; so at least the immediate area around the box would be plastic instead of carpet.  

What do you use to clean the things she has gone on?  Be sure it's a good enzyme cleaner and keep using the black light to be sure you find any accidents ASAP.  Unfortunately with some cats; you just can't leave soft things sitting out.  It's not an unheard of problem here.