I really admire your dedication to the games, it's similar to how I feel about them and also why I got into ROM hacking and still play even today. I hope everything goes the way you are aiming for!
The chance for shiny Rayquaza is supposed to be 1/200 in CosmicEmerald, though I can't quite remember if it's that exact number. It shouldn't depend on the clock, it sounds like you had bad luck there.
In a way though, I'm thinking that
accurate emulation really is the way to go overall for games that use a clock. When playing it in ROM format and with a clock system that doesn't rely on a physical battery, you could continue to enjoy time-based events indefinitely. From what I understand as of now, the cartridges always eventually need a battery change to continue to keep track of time, and on top of that you'd need to reset your save file from the beginning each time it's replaced (at least what I saw from multiple sources). With good emulation devices that have a clock (such as a PC, or an RG351P/M as just a couple of examples), you never have to worry about that. You can also much more easily back up your save files. Granted, I really do like the cartridge approach, and if I didn't have to worry about the time-based events not working, I'd go for that instead. It does indeed feel more authentic playing on cartridges, and the art and boxes add greatly to the experience.
If you go the cartridge route, I think a great idea would be to get a device that will let you back up your saves to another device so you don't have to lose all your work every time the battery needs changing. It would at least let you keep your old progress archived somewhere when you do start over again. I personally went with the
GBxCart RW. I don't know if it carries over the state of your clock, but it perfectly copied my old LeafGreen save file from my cartridge to my laptop. Even lets you backup the game itself if you wanted to do that.