As far as I know (and I have my coverage with them) Hagerty lets the owner select the value that goes on the policy. If the car is deemed a total loss then that is what you get from Hagerty, period.
Of course, a low valuation will mean a lower repair figure that will trigger a 'total'. They probably total a car at somewhere around 60% of the value insured.
Any additional loss (paper or cash) is either out of your pocket or recovered from another responsible party.
The key, of course, is that the value must be established
before a loss occurs. That is the nature of an
agreed value policy - which is what Hagerty uses.
I have always been able to increase my coverage with Hagerty (I do so every year or two) w/o any appraisal or additional photos (though I did submit new photos when I had a car re-sprayed).
As mentioned before, Hagerty has a valuation tool that may provide a starting point for deciding what value to place on the car:
https://www.hagerty.com/valuationtools/HVT/VehicleSearch
The results may or may not be your idea of replacement value -- but they are a guide and if you based your requested value using that tool I think it unlikely Hagerty would dispute your request. Indeed, it is in their interest that you carry adequate coverage.
But again, all I describe must occur prior to a loss -- once a loss has occurred you are under the policy & policy limits that were in place at the time of the loss.