I used pages from an old phone book for string quilt block & crazy quilting blocks. I'm not sure tissue paper is strong enough but it might be if you don't handle the blocks too much. I use tissue paper for tracing quilting motifs and then tape/pin/spray baste it on and quilt right through it.
It's very easy to rip out tissue paper and vellum so I'm not sure why you need it to wash out.
They didn't wash quilts in the old days--no commercial washers and dryers out on the prairie and too heavy to drag to the creek and back. They beat them like rugs or just aired them out so many still have the old newspapers they used for foundations inside of them.