On the surplus claim form you put owners name but then for mailing address you put
C/O Your Biz Name
Your Biz mailing address
There are banks that accept 3rd party checks, especially since its a check from a government entity (the county).
Here is a list that do accept 3rd party checks.
Now, instead of a Contingency Agreement + Power of Attorney Form, if you have the property owner sign an Assignment of Interest Form, then the county will put your name on the check because you are now the owner of the surplus funds.
Each county has their own Surplus Claim Form so the wording will be different, but for an example, here is a clip from Broward County Claim Form and how you fill it out.