The pucker is mostly the paint, not your tension. When you paint fabric with a watercolor wash, especally on something as dense as cotton canvas, the binder and pigment settle into the fibers and basicly set them in place. The fabric loses its drape and can't absorb the slight shifting that normal stitching needs. So every stitch pulls against a stiff patch that won't move with the thread, and you get little gathers around the letters. Two strands on a 24 is fine, that's not your issue. Going slower won't fix it either, though slowing down does help you notice when the fabric starts to gather before it's too late to undo. Some practical things that help: use a shorter stitch length so each stitch pulls less fabric, and work with a light hoop or none at all depending on which makes the fabric sit flatter. Some people score the back of stiffened fabric gently with a needle to break up the paint layer a bit before stitching, which gives the fibers a little flex back. Test that on a corner first though, since it can leave faint lines. A sharper needle also helps, it pushes between fibers instead of dragging through them.
Stitching first and painting after is honestly the better order for this kind of piece. The paint then locks the stitches in place and the thread becomes part of the surface instead of fighting it. The tradeoff is the paint can pool around the threads and change the look of the letters slightly, and you have to be careful not to gunk up the floss. But for letters that need to stay crisp over a wash, it ussually beats fighting stiffened fabric.
For washing, spot cleaning is really the only safe route with watercolor on canvas. Most watercolors are not truly washfast once dried, they can re_activate with water and bleed into the fabric around the painted area. A light mist test on a corner will show you fast if the color moves. If it does hold up to a damp test, still hand wash cold, no agitation, and dry flat. If it bleeds even a little, keep it to spot cleaning with a barely damp cloth and accept that a handled piece will show some wear over time.