I have done much better with the LAT than with the NYT. They also have electronic submission and quicker response and often give a more useful set of feedback (of course, I just got a rejection that was "nice idea, but we recently accepted someone else's version of the same theme" - so it goes). I don't use Crossfire, but it should be able to save into a format the Rich Norris can read - e-mail him about it, and my guess is you'll get a response pretty quickly.
Some observations: the LAT is much more theme-heavy, with five themed puzzles a week (M-F), almost no gadgets, and then a themeless on Saturday. That makes them more likely to accept a themed puzzle and less likely to accept a themeless than the 2 themes / 2 themelesses per week NYT (calculation based solely on number published and not accounting for number of submissions). I have gotten discouraging comments from Rich Norris about before-and-after themes and about puzzles with circles in some squares. Neither is a death sentence, but those are going to be less successful with the LAT than they might with some other venue, I suspect.
I have had very good experiences with the Chronicle of Higher Education (CHE). Patrick Berry reviews theme ideas quickly. If he likes them, he's helpful with the fill, and if not, he sends a quick and polite rejection, which we all know is better than waiting around (cue Huey Lewis "If this is it..."). If you have a nerdy theme idea, I would definitely run it by the CHE.
Finally, I note that every editor has been nothing but generous and constructive in response to my submissions. My hit rate isn't always very high, but I walk away feeling good even when I fail.
I am hardly a pro and am reporting only my experiences. Yours may be quite different.