One loud ticking after valve adjustment.

I ordered an airtex brand pump based on reviews of mechanical fuel pumps.

Uhhhhh...h'mm. Whose reviews, posted where? 'cuz it mostly doesn't matter whose name is on it any more; they're pretty much all cheap Chinese junk.

My favourite non-rebuildable pumps to use on the Slant motors are the large-body AC units like this one. Never had a problem running 'em with modern gasoline or anything like that.

I have the original pump that previous owner gave me. Rebuild kit is hard to find and expensive.

Who says? The kits come from Then and Now Automotive; see post here. Rebuilding those original Carter M2996S pumps is easy and kinda fun, even!