It's a new gun, so ....
You'll have to sign an affidavit stating what happened to the registered gun so they can mark that registration void.
Then I'm 99% sure you'll have to go through the permit process again.
To be safe, you should have Riuger ship the handgun to your FFL, not direct to you. Legally, you can ship a gun to a gunsmith/manufacturer for work and have it returned. The returned gun will not be the one you shipped. So, use an FFL.
Once the FFL has the gun, it's like any other acquisition: get the serial number from the FFL, then run to HPD to apply for another permit.
I guarantee the lawmakers never imagined this scenario (they don't seem to understand much about guns to begin with), so you're stuck with:
"(a) No person shall acquire the ownership of a firearm, whether usable or unusable, serviceable or unserviceable, modern or antique, registered under prior law or by a prior owner or unregistered, either by purchase, gift, inheritance, bequest, or in any other manner, whether procured in the State or imported by mail, express, freight, or otherwise, until the person has first procured from the chief of police of the county of the person's place of business or, if there is no place of business, the person's residence or, if there is neither place of business nor residence, the person's place of sojourn, a permit to acquire the ownership of a firearm as prescribed in this section."
They ask for the handgun serial number for the permit for a reason. I doubt that reason is known or makes sense, but the result is your original permit was approved for one numbered Ruger LCRX. The serial number can't be changed on the permit after approval. The only path forward is to apply for a new permit.
If someone at HPD (Suzie) has a "work-aroiund", it would be nice if you shared it, but so far, I've not seen anyone else post one.