Honestly I think if the base of the cars, like suspension and aero is handled, the tire will work without major changes. Other cars will just provide context.
I don't see anything in it that would produce a big inaccuracy inherent to just one car, apart from the heat and wear stuff. If it's off, it's gonna be off for all of them in the same way.
Sadly vanilla AC heating just doesn't cut it, but it's your choice if you want to use CSP heat. I think it's desirable for racecars, but myself because I make roadcars and want to maintain vanilla compatibility, I chose not to.
If you too choose not to, it might be necessary to settle for a level of inaccuracy especially in a race situation.
A lot of tire stuff is a guesstimate sadly, but they are all round and black after all.
I myself use load curves because like you said, the precise result you want is easier to obtain, and it has less limitations. These cars are making almost 1.0 CLa in downforce and some of them also go very close to, or 0 load in some situations, so using load curves with a more appropriate shape would probably improve the behavior and laptimes without sacrificing anything.
Also, I believe, from findings of other members of the community, FALLOFF_LEVEL=0.85 should probably be a little lower, perhaps FALLOFF_LEVEL=0.78 or a little lower. There is some evidence to point towards it.
The reasoning is that because while the 15% grip loss from slip is indeed probably quite true to real figures, there seems to be an additional perhaps 5 - 10% loss or so from the rapid heating of the surface of the tire during use.
Since this surface simply doesn't exist in vanilla AC heating (It's some layer(s) below to my understanding, not the very top layer) and often it is not configured to heat up realistically; that being very rapidly up then back down after the corner; the grip level for example during locking of the wheel or in a drift can be inappropriate. I'm still playing around with the values myself so don't take it as something which is definite.
I haven't looked at CSP heating enough to know if it introduces this true top layer and fixes this issue; if it does, great, then perhaps no modifications would be needed.