If you start with a file that has a native resolution of less than 360 ppi at the desired print size, you upress to 360 ppi using PS, LR or AIG, and then send the file to the Epson printer and check "Finest Detail," will the printer pipeline not upress from 360 to 720? If so, would you not be better off upressing in PS, LR or AIG to 720 dpi?
With AIG, yes, because AIG will attempt to add more resolution where there was none, to begin with. As long as you keep the resulting filesize below 4 GB (TIFF limitation).
Example, you have a narrow line, say a distant powerline or a twig or a crack in a surface, the other methods will make that line 6x as wide when scaling 600%. AIG will try to keep it narrower and sharp at just 4x times as wide, thus with higher resolution. This will not make a huge difference, but in some of the details it does show. And that is before any output sharpening is added. With more pixels, one can do a better job of sharpening for output.
I have an image example I'm willing to share.
Now, before you start inspecting the level of detail, make sure to zoom out to the printed dimensions, so use:
100 * Display_PPI / Printer_PPI
as the display zoom percentage to watch it at the printed output size (@600 PPI or 720 PPI).
There will hardly be a visual difference, because the display pixels are the same size. But now, realize that the 600/720PPI print will have almost twice the resolution of what is needed to satisfy our average visual acuity. It will be sharper.
An excellent print can be made (almost as good as when starting with the full-size original, not this downsampled version of it). The downsampling did lose some detail (because it became smaller than 1 pixel), but AIG did a fine job of restoring the impression of detail.
Cheers,
Bart