I *like* the resinous taste. But then I'm weird that way.
By the way, the best Eugenia is probably Eugenia candolleana. E. neonitida is also highly regarded as you see above. Very high quality juice Eugenias are E. victoriana and stipitatas. These are quite sour and needs sugar. Has lots of 'tropical' taste. Can find most of these, eventually, from http://www.fruitlovers.com/seedlistUSA.html or Jim West' place.
Depending on quite how warm you are, I'd probably tell you that you should prioritize on getting Jaboticabas. A fast fruiting red one, and put the heavyweights like the grimal, plinia edulis, myrcaria aureana in for that day fifteen years down the road.
I think you may be definitely too cold for the obvious fig analogues such as white sapotes or sapodillas, in terms of sweet, soft, mild.
How cold does it get where you are? Do you have any other fruit trees?