Your idle speed is correct. I suspect the stator, since you know the reg/rec is new, and the battery is not charging.
To test your stator:
Start your bike and get it up to operating temp. Then shut the bike off.
Unhook your stator plug from the reg/rec. It's the one with three yellow wires.
Picture each of the yellow wires as A, B, and C.
Put your multimeter in VAC mode, and put the probes into the stator side of the connector wires A and B.
Start the bike.
Your multimeter should read around 25 VAC at idle, and upwards of 60 VAC at 4500rpm.
Now test wires A and C, and then test B and C.
Your looking for consistency among all three pairs of yellow wires. If one pair reads different than the other two, your stator is bad.
Also, inspect the condition of the wires and connector. Any signs of burn or severe heat? That's a problem too.
Here's my test results from a while back.
Try that, and let us know what numbers you get.