I solved the counter space issue by putting my FoodSaver on a shelf above the counter and under the cabinets. I use it enough that's it's a pain to haul it out every time but not enough for it to take up counter space. It's a shallow shelf near the wall and most of the time I don't even have to take it down to use it. Still have the counter space and the FS is always there.
The paper towel method works well but I find myself freezing first before sealing if the product is to be frozen.
No basement or attic here. When I built this place I was poor (Maybe not poor but pushing it to the limit and I still am
) and slab on grade was the way to go. At times I wish I had a basement but at other times I'm glad I don't because I'd just store stuff I really don't need. I've got too much junk as it is. But as we all know it's our junk and we simply can't part with it. Not to mention that as soon as we get rid of it we'll find a use for it.