After reading these answers, yesterday, I experimented and found cooking chopped up CHERRY TOMATOES and CELERY, then blending them together, created a suspended mass, not runny. Adding that to runny raw salsa might work for what one has in mind. My plan is to have regular raw tomatoes for the main mass, at the end, but cherry tomatoes seem to be an interesting possibility as a filler.
When I keep containers of cherry tomatoes above the fridge, some, eventually, shrink and shrivel. I hypothesize if cherry tomatoes are left to dry more to shrivel stage, they could create a thick paste of fresh tomatoes when mixed with a little fresh tomato in a cuisinart spin. That might be an addition to the salsa that could absorb some of the water, since the cherry tomatoes might continue to absorb.
I just added some Bob’s Red Mil Organic Amaranth Flour to the liquid I strained, and I found when I boiled it into the liquid, it thickened, and the taste was still good. Since amaranth is from the same land as tomatoes, originally, maybe that helps the flavors to blend. I am always looking for ways to make salsa a more complete food.
FYI, I, also, freeze containers of boiled amaranth whole grain to add to other things, ongoing. It can be gelatinous, and as a vegetarian, I am always on the lookout for such aids. I love the taste added to things as they are cooking, i.e. hot milk, soup, etc...mild with natural energy. I find putting a Viva paper towel over the strainer lets me rinse the amaranth whole grains with it not falling through the mesh, being so tiny. I am going to look for a way to make the cooked grain a paste, which might, also, be a good thickening aid for raw salsa.
BOTTOM LINE: As an answer to the original question, here, I would advise straining the too-wet raw salsa, then take that juice and bring it to a boil with amaranth flour as a thickener. Then just mix that back into the raw salsa, after cooling. I gave the salsa I made to the husband and he said it was the best he has ever tasted. So, slipping in amaranth flour does not dull the taste, if maybe it might blend it a little.