Just a general question: do most publishers have the same form rejection letter for every rejection? Lightspeed states in their guidelines that they will only say "send more" if they actually want more. Is that common among publishers or do most just respond with "hope that you'll keep us in mind in the future" and similar taglines to keep a polite tone?
Yes, most publishers just send the same bit of text for every rejection, but that bit of text varies from publisher to publisher. If Lightspeed only want a partial manuscript, that is unusual. Most that I've come across want the whole story, although Heroic Fantasy Quarterly do the same as Lightspeed.