Yeah, I think it's a bit cheeky, sorry. You could maybe ask them to do the initial checking 'I'm doing X for my birthday with my friends, I know the girls said they'd like to do it again, can you send them a message and let me know how many are definitely in,' but can't expect them to do the whole thing as a separate booking.
I also don't really get the logic of the activity/restaurant refusing one booking of 35 people but being happy to accept two bookings, of 20 and 15 people, at the same time.
If anything, one big booking is surely easier for them to manage than 20 groups of 2 people.
You've got the advantage of time on your side, just start organising early - send a message now saying I know it's way in advance but there are a lot of people coming so we need to book early, but the positive is by the time we get to December we will have forgotten we'll have paid and it will feel like a free night out!
Give people a cut off date to respond and, key, MAKE SURE YOU GET THE FULL AMOUNT IN ADVANCE. That way, if people drop out, it's not your issue to keep ringing and rebooking for different numbers, they just have to accept they've lost the money.
Make a spreadsheet if you want. It doesn't have to be that complicated, just name, tick box for activity, tick box for meal, tick box for coach, although tbh I'd be tempted to just get people to arrange their own transport and say 'we're meeting in X at X time.'
The majority of the stress in organising something is getting people to commit to coming and paying. Once you've done that, even if it takes a month or two now, you can chill for your actual birthday.
I highly doubt that, if presented with a fully paid group booking in February/March, for December, many places will turn you down. They'd probably be delighted!