Is it possible for the 4x9 grid of decoded callsigns to be sorted by
priority?  Often I'll see a call go by that got highlighted, but on
the next sequence (i.e. 30 seconds later), even though the call was
decoded again, there can be too many callsigns to put in the grid, and
the one I wanted to see again no longer fits.  This means it's not
there to click on.  I could be in the middle of a QSO which would
prevent me from clicking on it when I saw it go by the first time.

I'd prefer the highest-priority calls to be in the upper-left-hand
corner, while the lowest priority calls are in the lower right corner.
Whether they are sorted vertically first then horizontally or vice
versa doesn't matter to me.

Short answer... NO

Long answer... Any sort of callsign sorting will require that all decodes have been processed and delivered by WSJT-X before JTAlert can produce a sorted display. That could be several seconds of dead (non-display) time depending on you PC capability and how busy the Band.

If you're overflowing the 4x9 grid with callsigns, there are a couple of options...

1. Apply one or more Alert filters when you're on a busy band to remove the Callsigns you're unlikely to want to work, say filter out the B4's or Callsigns not generating alerts.
   
   
2. Use the Decodes window, it has no limit on the Callsigns displayed in a period, unlike the main JTAlert window. You can even view decodes from a previous periods. Callsigns in the Decodes window obey the same mouse clicks as the main JTAlert window.
   

de Laurie VK3AMA