That's great news and thank you for confirming the frame advancement that occurs when the day changes. I wonder if 3 frames will hold true for every game cartridge. If I ever have a day change RNG to do, at least I'll be prepared.
I've always avoided change of the day RNG times, but haven't had trouble on catches for change of any other hour. You could be on to something here. Let me know how it turns out. You could try a different RNG time that avoids a change of day, too.
The second post of the help thread has a hidden section with advice on how to do the roamers. It doesn't say anything about Lance advancing the frames. I didn't use the RadioSeed program for my Roamer RNG, since it reported incorrect delays to me. But I did use the radio to advance.
Be careful how you advance the radio. Always start with your radio saved in the very centre. The first hit on Pokemon Search Party button counts as one, but then you drag to the side of the circle, never the centre of the circle. Dragging back to the centre is touchy. You could get an extra frame advancement if you do it wrong, but dragging to the circumference is more stable. On the last push of the Pokemon Search Party button, do not drag to the side again. Leave the station alone and go straight to talking to Lance.
I believe that post 2 on the help thread says something about the red Gyarados's IVs being generated the same as with chained shinies and doesn't give much help for how to get beyond this problem. I haven't successfully captured the red Gyarados that belongs to the game story, though I could capture a shiny gyarados that isn't part of the game story. Sorry I couldn't be of help.
Oh, and when you get to one before your target, you leave the Pokegear and step into the circle of your choice, say yes to Cynthia, watch the show and wait for your pokemon to arrive in your party.
Sorry, I wasn't actually at the desk this last hour.
You should save inside the centre of the circle (be aware that once you are saved there, you have no choice but to finish your RNG project because you can't leave until you choose a pokemon). You use Method 1. Then you do the same steps as with a standing legendary, except you have exactly one frame to hit. Make sure you have a low frame to hit, because you can't use the radio to advance, only Elm or Joey.