The only space I have large enough is the carpeted living room. I use T-pins and pin backing to carpet. I lay the batting on top and smooth out. I then smooth the top out and pin it to the carpet. I use safety pins to hold it all together. Only occasionally does a pin get stuck in the carpet. I have pinned a large full quilt this way and it works for me.

I too wouldn't use duct tape. While I know you wouldn't like trying to get it out of your carpet, it may cause a terrible mess on your quilt. I would look into using the library, or a community center, your church, or a sewing circle that may be close to you. I've use packing tape and I have used pins. Figure out what works best for you, I'm with you though, getting down on the floor is not as easy as it was before 2 knee replacements.