Hi and welcome to the board. You've gotten some good answers so far and I agree your issue is not thread. There shouldn't be any reason you can't use many different types and weights of threads on your sitdown LA. And there are many, many things that can affect your tension, from poorly wound bobbins to bobbins out of round to a thread guide needing to be tweaked a fraction of an inch rotation. While I quilt on a rack mounted LA there are some similarities to sit down but one we can eliminate from the get go is having the quilt loaded to tightly on the rack.
LA tension is much fussier than domestic and I think you need to pinpoint if your issues are on top or bottom. Can you describe what tension issues your are experiencing? For example pokies of bobbin thread color showing on top or getting eyelashes on the bottom. Are the issues intermittant? Do you get good tension when you first start then suddenly it goes wonky on you?
I agree a Towa is a good investment for many but even though I have one, I rarely pull mine out. Have you viewed Jamie Wallen's you tube about bobbin tension on a LA? This is a good place to start:
https://www.youtube.com/watch?v=Q1mRhcquZTM
Tweaking tension is something you have to do much more on a LA than a DSM. I check my tension with every bobbin change and periodically mid bobbin, you never know when you get a blob of lint stuck in the tension spring so when using cotton thread or I have a flannel backing (both make a lot of lint), I check frequently. This is one reason I don't use cotton very much for quilting. I prefer to stick with polys that don't make any lint. Please don't be frustrated, it takes some time to get used to the extra bit of futzing about with tension on a LA but once you get it, it will become 2nd nature to you and you will get into a routine. Also don't limit yourself on threads. There are so many wonderful and pretty threads on the market and they should sew fine in your machine, through trial and error you will discover ones that you won't like for whatever reason but don't stick with just one brand/type of thread as different styles of quilting dictate different types of thread. You say you do a lot of applique and I will often use invisifil 100 wt polyester or monofilament thread to ditch applique, then a different thread to do background quilting.