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That whole idea of 'reasonableness' is so reassuring. So much of what happens here does not seem reasonable and it's good to know that it's a key component of these hearings.
I have a lot of reading to do but I think RA followed by forensic examination of accounts, followed by either RTM or full Enfranchisement (if people are willing to contribute) is the way to go. It's like herding cats right now though. Everyone's been burned by FTT (or more accurately, by their own failure to prepare, but that's a truth people don't want to hear) before and they're very nervous about trying their luck again.
The test of 'reasonableness' is the one that the First Tier Tribunal will always apply, and it will always be looked at in the context of the lease.
If the judgment was that the lease has no provision to make a charge for parking, that's pretty final and there's little room for the freeholder to argue otherwise, beyond appealing the decision at a higher court - which it seems they didn't bother doing.
Other than seeking a court injunction (rather than FTT judgment) against the freeholder the obvious options would be to go for RTM / enfranchisement, as it seems you're already considering, or apply to the FTT for appointment of a manager.