Thanks for the replies. I double-checked to see if it was in valet mode. It is not. The LED was not lit solid. I turned key on, then off, then pressed valet button. This put it into valet mode, turning the LED on solid. I then took it back out of valet mode, the way it has been all along. I have since learned some more information to pass along, which will hopefully help you all help me.
1) I decided to try remote starting with the hood open, just as a way to get information and confirm/rule-out things. Guess what... it started with the hood open, but does not start with the hood closed. I mis-stated previously that the hood switch is wired into the fuse box. I was wrong about that. A different, unrelated wire is hooked into the fusebox, I don't know what it is, but apparently it's been there a while. The hood switch wire in fact goes behind a type of black plastic cover/conduit piece on the upper firewall. I can't find where any wire related to the alarm/remote start actually goes through the firewall, but I'm not sure that's an issue. Everything was working fine before the mechanic worked on it. Whatever happened must be accidental while replacing the fuel injectors. So, can anyone think of what would cause the remote start to work with hood open and not with hood closed? That seems like a very specific clue that may help solve the puzzle.
2) I've been reading the documentation that I can get my hands on related to this unit. I found the docs for Python 1500ESP and for the "553A" (instead of mine, which is 553P). Those mention a "tach" wire that can be tied into a non-red wire on a fuel injector. I looked and found a (dunno the correct name) wire connector attachment on the non-red wire of the fuel injector for cylinder #1 (which is the easiest to reach). There is no wire connected to the little add-on wire connector, however. I looked for a wire that seemed loose hanging around somewhere that looks like maybe it belonged there, but I don't see one that stands out to me. I don't know for sure that my unit ever had that wire connected, but why else would there be an add on wire splice connector on that one fuel injector? Would that wire being mistakenly disconnected maybe cause the behavior it's exhibiting (starting with hood open, but not when hood is closed)?
3) The extra chirp that follows the normal arming chirp... I was curious to test if that maybe would resolve with the hood open like the remote starting did, but that extra chirp still sounds regardless of hood position. Is there some way I can figure out what "active input" it's detecting to cause that extra arming chirp, or might that be related to the missing injector "tach" wire?
I really appreciate the help being offered.