Thanks for the suggestion. I have never tried 60/40 synthetic/cotton for shirts. I have an old (circa 1970) Sierra Designs mountaineering parka that is made of 60/40; the cotton is supposed to swell up when wet and close up the holes between the threads. This is claimed to make the garment more water resistant. I also have an old (circa 1958) 2-person REI (Co-op in those days) tent made of similar fabric. It was, still is in fact, single-walled, weighs about 5 lb with poles and cost about $25. Both of them served me well for a long time.
I'll try the 35% cotton shirt; I use the shirt mainly for sun protection and not warmth. And, there are a lot of part-cotton shirts available in thrift shops.