My two cents worth...Buy the biggest/ best cooler you can, then bring lots of ice with you,( blocks last longer) and buy more as needed since you will be at Bullfrog anyway if you were planning to rent freezer space.(not available to my knowledge) Dedicate one cooler to just fish so you don't open it as much and you will have no problem.
There are more "reasonable" priced coolers that hold ice quite well, not quite as long as the one Lake Bum mentioned and the others that were referenced in tests. I own 3 of the brands mentioned (and they are good,) (luckily I got them at the very right price) and yet my buddy uses a cooler that costs a third as much (Got it at Costco) and he uses it for houseboat trips as long as 10 days. He does not have to run to the marina that often to top it off with ice and we bring back plent of fish always in good shape.
Love my Yeti coolers, but if I were buying today I would also consider other brands. I know nothing about the one linked above, but there are reasons why everyone compares their cooler to Yeti - not the other way around.
I also am unaware of any freezer rental in Bullfrog.
We shore camp for 5-7 days up north. We will have plenty of coolers packed with block ice frozen water bottles and will use dedicated fish cooler (Yeti). Will also eat fish in the order it was caught. We did not have problems last year but we had a buddy leave early with early caught fish. Just wondered limit for fish on ice...don't think i would want to exceed 5 days before freezing.
I know that people can eat fish that is way more "aged" than ever thought possible from my last 2 big fishing trips to powell. One week on the water with 6 friends on a rental houseboat, last week of april. Caught so many fish that our coolers couldn't possibly handle them. One guy who will remain unnamed didn't give a hoot about everyone's concern about warm fish. He took them all home and being the nice guy he is offered all of us his bounty before taking them. I will only say that when you see a raven turn his nose up to a striper on the beach any smart person would have to agree. We never got a report of any one getting sick in his family so maybe all this worry about which coolers to use is moot. wink wink but true story