Do you have to recheck your luggage after going through customs or do they just transfer it to the next aircraft?

Yes.

I'll be doing this in 5-6 hours. I'll report back.

But unless you are coming from an international city where you go through US customs and immigration, you will always have to. Example is Nassau, you go through US c/i there. Same with some Canadian cities, Dublin, etc.

Yes, after immigration you'll go down the escalator into the international baggage claim. Get your bag and head out but turn left for connecting flights instead of turning right for the arrivals exit. You'll see ticket counters on the left where they can re-check your bag for the domestic leg and there's also a TSA checkpoint that you'll get funneled into. It's pretty straightforward.

Awesome, thank you.

Thank you