"The settlement checks were written to Charles Schwab in our name and our new IRA account."
If by "our" you mean more than one individual, there is no such thing as "our" IRA account. IRAs can only be owned by a single individual.
The deposit would typically be considered to be a nonreportable restorative payment to the individual's IRA. The handling would be similar to a nonreportable trustee-to-trustee transfer of an IRA where the funds are never made payable to the IRA owner. Because there was no actual distribution to roll over, the deposit can't really constitute a rollover that would be reportable on Form 5498.
