Where to start? Obviously this is way different now than when your troubles started last year so I think it's prudent to begin with the basics again.
From your description just so I'm at the right place here, the bike shuts down and dash and lights flicker off and back on rather than dim so you are momentarily loosing power totally but then it immediately comes back. It's just not stalling out like a lack of fuel or turning off like a kill switch would do.
Places I'd start is the power which you've done. Throw in a quick check to the breaker if you've not done that yet just to check it off. With as much as you've had apart, confirm all the connectors are good and tight.
If you know someone with another bike, swap the flasher relay that some druggie engineer designed and wired up. It's not worth buying a new one yet just to prove it. Strange, but hold in the clutch lever.
What I find odd is momentarily loosing power all together. One of the normal control methods should ground out a feedback signal from a sensor to the ecm and just quit firing rather than totally interrupt the power.
On a related note, do you have the part number for the IAC that works from a Razor?