Let's face it - running in the sunshine is going to be a test for any garment. If you were running naked, you would be sweaty and would cool down through evaporative heat loss, so why would you expect that running in a synthetic shirt is going to rectify that?
Adding a further layer of insulation with a string vest vest underneath will make you even hotter, increase sweating and compound the problem, although the mesh will stop the shirt sticking to your back.
I hike hot, and therefore vary my combinations of base and mid-layers according to the conditions during the day. Thin silver-impregnated (Berghaus polyester teeshirt (short or long-sleeved depending on the expected heat and doesn't stink after several days use). If is going to be cooler, then a RAB merino-polyester mix (dries much quicker than plain merino) long-sleeved zip top baselayer. I will use a heavier weight version if it is colder still.
I then add a simple Montane windshirt over the top if I want some more warmth e.g. to cut the wind out, may be with a buff and or hat. If this is still not enough, then the windshirt is replaced with a RAB Alpine Vapour-Rise jacket (a brilliant piece of kit). For more warmth would change the jacket to a Norrona Alpha Raw fleece (almost a fleece version of mesh - fantastic wicking) and put the windshirt back on or the jacket. In winter conditions, I wear the much warmer RAB Guide Vapour-Rise jacket and trousers, usually with just a merino-polyester base layer underneath.
Every layer is breathable and without a membrane. I find windblock-type membrane fleece or soft shell garments much too limited in their suitable temperature range and don't use them any more. Hard shell garments only come out if it rains. Multiple thin layers in various combinations definitely work best for me. The time garments take to dry after washing them is a good indicator of how quickly they will dry out on your skin after getting wet from sweat.
At times of course I still sweat when wearing the lest possible insulation, its unavoidable, but at least my system allows it to dry out as quickly as possible.
Then there is the topic of rucksack designs to mitigate sweaty backs ... at least we have come a long way from the old plain canvas backed sacks!