I've never used Aqua solvy, but use a product similar to Aqua Mesh, for free standing lace (different brand, looks identical to the OESD product., but lots cheaper, purchased in bulk, off the Internet) The texture is like a loosely woven fabric. I use matching thread in the bobbin, usually a trilobal polyester, or if I'm making white ornaments, I use Bottom line, or other bobbin thread. I also thread the pigtail on the bobbin case.
I get a thread break every once in awhile, but just back up to the break & start up again. There is so much of the product left in the lace after rinsing, that I've not have unraveling so far from doing this.