Would Crisis Force for the Famicom/NES count?
It's on the list, though I imagine that more people here would probably prefer the inclusion of Recca over it.
This thread lacks Allumers Mad Shark

Yes, it certainly does.

(I'll add it to the "others" list, though, just in case.)
has Gazelles Air/Akuu Gallet been mentioned?
It has been, actually, though I forget to add it; I personally wouldn't call it a gem (more of a brief footnote in the genre's history, if anything), but I'll throw it on the secondary list as well, since I know it has its fans.
Could "Boogie Wings" fit here?
It tends to get a mixed reception here, but I'll throw it in.
adding Bio Metal to my suggestion list...I'm not familiar with its sequels
Looks like you beat Rob to it!

By the way, what do you mean when you say "sequels"? I wasn't aware of any, though IIRC Athena put a "mini" version of it onto one of the Dezaemon titles.
Crimzon Clover too, which didn't made up in the lists
That's because it's a doujin (along with a few of the others you mentioned), and for the moment I'm keeping those separate from the current conversation. Though I am wondering why it didn't end up in the "others" list along with a handful of other doujins...well, I'll be reorganizing all that eventually anyways.
Dragon Breed, Cosmic Cop/APU Gallop
Hmm...Dragon Breed is an interesting choice, though one might argue that it's not technically a "pure" shmup...I'll add it to the top list anyway, though for now I'll keep Gallet on the bottom until it gets put through the wringer a bit more.
First post re-updated.