I doubt anything could make this fig even compete with a number of more common varieties.
And Brent - I grew and fruited JH Adriatic and a number of other figs with less than an hour of sunlight against the north side of my neighbors house (posted pics all over here of it) and they tasted awesome. Like, 8/10 or 9/10 awesome. So, I don't buy for a minute that 6 hours sun - which is by definition "full sun" (6-8 hours direct) - would have made this fruit taste better.
I think it is best to accept that "real" Brown Turkey figs (i.e. plain old BT, not EBT or others which may not be genetically related) taste like crap and are generally worthless.
I am sharing cuttings with someone I trust to grow it well in a hotter sunnier and potentially dryer climate. I'm sure the same results will be had but we will see. I've sent cuttings of this tree to others. The only feedback I've gotten suggests it tastes watery and bland there as well.