£400 sign up bonus – refund option?

I agree. The easiest and safer option is to just book the extra night. Especially with the extra £100 benefit, why not!
Regarding your original question – I struggled with the same issue when booking a flight using the credit in Aug. I tried to get clarity from a number of Amex reps, but nobody could give me a definitive answer. Tried on HfP too but did not get a clear answer.
I had, although, come across a few online posts from Amex Australia(?) where people had reported receiving the full refund (£420 in your case) and the credits not being reversed. So in your case, that’ll mean you get back £420 and that’s it. So you end up with +£400 net.
But that was an old and non-UK post, so rely on it at your own risk.

as02 wrote:

Especially with the extra £100 benefit,

This is against the FHR terms…

“Back-to-back stays booked by a single Cardmember, Cardmembers staying in the same room or Cardmembers traveling in the same party within a 24-hour period at the same property are considered one stay and are ineligible for additional FHR benefits (“Prohibited Action”). American Express and the property reserve the right to modify or revoke FHR benefits at any time without notice if we or they determine, in our or their sole discretion, that you may have engaged in a Prohibited Action, or have engaged in abuse, misuse, or gaming in connection with your FHR benefits.”

So you probably want to contact the hotel and explain you don’t expect two sets of credits. Or maybe see if there’s a cheaper option than FHR for the second night. Again if you contact the hotel they’ll likely want to keep you in the same room as it’s less cleaning.