Another poster stated that finest detail enabled a higher quality uprez to 360 dpi by the driver, so that should have zero effect if it's on or off when printing targets.
There is no best setting for targets. You need to do testing to determine what suits your needs vs print speed and possible ink consumption i.e., 1440 vs 2880 and HS on or off. This needs to be done for each paper, and if it's non-epson paper, you need to find the paper setting that gives the best dMax (black) and saturation results with no color adjustment.
A good thing you can do, is really understand and perform head alignments and nozzle checks. They are often a reason for a profile "shifting".
According to Epson, the 3800 is calibrated well enough to use the same profile for 1440 and 2880. I have not heard confirmation of that, but on epson papers, it is likely true.
That being said, I would consult your profile service for advice with their targets and the 3800 settings before printing them out.