I agree with utility, don't know why the electrician specified 6-200 A Meters, perhaps he was a little confused on the code or the 100 foot specification to the first site.
One method of serving your needs is to install 6 ea - Main Breaker Panel with Feed-Thru Lugs. Five panels would have a 150 A Main, the sixth would have a 200 A Main. The panel with the 200 A Main would be used to supply one run to RV Sites and the laundry circuit (s). Each of the 150s would supply one run to RV Sites. There are other, more expensive methods for the service.
For this type installation, you will have one utility meter, a CT Meter.
Each service drop should consist of 3 ea - 3/0 THHN Copper.
The run to each site, unless runs are of excessive length or begin an excessive distance from the service, or both, should consist of a quad aluminum cable suitable for direct burial, normally 4/0, 4/0, 2/0, 4.
Each site pedestal would have feed-thru lugs similar to Milbank U5200-XL-75. Be sure to specify Loop feed-thru lugs.
Note: This pedestal includes a 20A, 125 volt recep that each site is required to include.
I can provide other services at additional cost such as a sketch of the service and/or a sketch of the service & sites. Let me know if interested and I will send a quote separately.
Please let me know if you have any other questions.
Good luck with your project.