I have a two handle, high arch Moen Banbury, chrome faucet with an after-market side spray attachment. After shutting off the house water for some repair/drain work, now there's no water pressure through the kitchen faucet at all (including the side spray).

So far, I've removed the aerator, flushed the lines (good water pressure from both hot & cold stem lines), replaced the Hot/Cold cartridges, removed the spout to check for debris (no diverter there, I found it by unscrewing the top of the side spray unit).

The rest of the house has great water pressure - all the way back to the attached garage/laundry/laundry tub, including front sprinklers, front and back hoses.

Any ideas?

The hot and cold water lines come to a tee or cross where the spout are and there could be something caught there and you could take the hot cartride out and cover the hole that's there and then turn the cold side on and backflush the cold to hot side and then the same for hot to cold side of the faucet. But remember to turn off the side that you have pulled out the cartridge.try that and let me know

Not a tee but close enough. The hot and cold combine in the valve body.
Let's see if I understand all that you have done. You have opened up the hot and cold sides, removed the cartridges and turned the water back on to flush out the supplies and open valve body and found them clear. Is that correct?
When you had the cartridges out did you inspect the inlet ports for blockage before you replaced them?
Here's what I think has happened. In repairing the plumbing some mineral build up in the pipe walls was disturbed and are now clogging the inlet ports in the cartridges, that is if you've flushed out the supplies. Remove the cartridges and check for blockage. Let me know what As a last resort simply replace the cartridges. You find. Good luck, Tom