Yes often 40-45%/ any common liquor (vodka, rum, brandy) is suggested for tincturing, but I find that really for fresh plants that are quite watery (such as violet) a higher alcohol is needed to properly preserve it.
I would suggest trying the straining process without pressing it, yes. Maybe try to strain it through 2 nut bags at the same time or something of the like. You could gently squeeze it, but maybe not too hard. It is entirely possible that this next batch would be okay. The goopiness is a good sign in many ways, because that is the bountiful mucilaginous compounds that are in violet. Maybe keep this batch in the fridge to help with the shelf life.
I think that tea would be of similar benefit, it depends on what the tincture is meant for. If you are to take a tea of the leaf, then I would lean toward a cool overnight infusion to preserve the mucilage, but if your herbalist has you taking violet for the saponin content, then I would try steeping in boiled water of better as a tincture afterall.
To make tea that would be close to the same dosage as 1 dropperful of 1:3 tincture 2x/day, would be 1-2 tsp of chopped fresh plant/cup and 2 cups per day or 1 g of fresh plant/day.
Wishing you the best of herbal luck. I’d be interested to hear about how that second tincture turned out!