Thanks very much for the advice! Hopefully I'll be able to get on the bus if 1000s of people think the same way!
No worries. If the train is busy then you might want to make sure you sit in the front carriage and then when you get to Uckfield just immediately leave the platform and turn left on to the pavement and the bus stop is there on the same side of the road. The stop is just a twenty second walk from the platform. So hopefully you can be first in queue for the bus. Although there are three buses an hour so i doubt you will have a problem getting on a bus.
Taking the Uckfield option is the quickest and most convenient and is also one of the most frequent bus service with three buses and hour so hopefully the fact that it has more buses will mean that it can deal with larger amounts of passengers better.
Also at the bus stop outside of the railway station in Uckfield you can take any 29 bus as the 29 for the opposite direction stops on the other side of the road. But if you take a 29A make sure you check that it says Brighton on the front of it. This is because the 29A for both directions serve the same exact bus stop on the same side of the road and also come at around the same time as each other every hour.
One risk of trying to get on board at Uckfield may be that the buses (other than the first two of the day) on route 29 originate from Tunbridge Wells so could easily be full at Uckfield if lots of people have the same idea. However, the 29A starts at Heathfield.
Other buses to Brighton run from Crawley (271 / 273 combined hourly), Horsham (17 hourly) and East Grinstead (270 hourly).
Even the combined capacity of all these buses is less than one class 700 of course.
The bus from Uckfield to Brighton runs three times an hour so it should not be much of an issue if it is too busy. In the event that the first bus is too full there will always be another bus only a short wait later. So i think this option should work fine.
But as you say taking the 29A might be a good option is this should be a little bit quieter than the 29 buses. Alighting from the train at Eridge and getting on the bus there is another good option to increase your chance of the bus being quieter. Although from Eridge you only get 2bph instead of 3bph.
I believe this is the full list of options available to travel to and from Brighton on that day:
• Take a train to Uckfield (1tph) and then take the Brighton & Hove routes 29 29A to Brighton (3bph).
• Take a train to Buxted (1tph) and then take the Brighton & Hove route 29 to Brighton (2bph).
• Take a train to Crowborough (1tph) and then take the Brighton & Hove route 29 to Brighton (2bph).
• Take a train to Eridge (1tph) and then take the Brighton & Hove route 29 to Brighton (2bph).
• Take a train to Tunbridge Wells (2tph) and then take the Brighton & Hove route 29 to Brighton (2bph).
• Take a train to East Grinstead (2tph) and then take the Metrobus route 270 to Brighton (1bph).
• Take a train to Three Bridges (6tph) and then take the Metrobus routes 272 to Brighton (0.5bph)
• Take a train to Crawley (2tph) and then take the Metrobus routes 271 272 273 to Brighton (1or2bph).
• Take a train to Horsham (2tph) and then take the Stagecoach route 17 to Brighton (1bph).
• Take a train to Etchingham (2tph) and then take the Compass Bus route 231 to Heathfield (0.5bph) and then take the Brighton & Hove route 29A to Brighton (1bph).
• Take a train to Tunbridge Wells (2tph) and then take the Stagecoach route 51 to Heathfield (2bph) and then take the Brighton & Hove route 29A to Brighton (1bph).
• Take a train to Tunbridge Wells (2tph) and then take the Stagecoach route 51 to Hailsham (2bph) and then take the Brighton & Hove route 28 to Brighton (2bph).
• Take a train to Hastings (2tph) and the take the Stagecoach route 98 to Hailsham (1bph) and then take the Brighton & Hove route 28 to Brighton (2bph).
• Take a train to Hastings (2tph) and the take the Stagecoach routes 98 99 to Eastbourne (4bph) and then take the Brighton & Hove routes 11X 12 12A 12X 13X 28 to Brighton (10bph).
• Take a train to Barnham (2tph) and then take the Stagecoach route 500 to Littlehampton (2bph) and then take the Stagecoach route 700 to Brighton (6bph).
• Take a train to Arundel (2tph) and then take the Stagecoach route 9 to Littlehampton (1bph) and then take the Stagecoach route 700 to Brighton (6bph).
Note the Buxted and Crowborough options both involve a fifteen minute walk between the railway stations and bus stops but with all of the other options the bus stops right outside of the railway station so no walking is required.
I think the Uckfield option is still the best option out of all of these. This is the quickest of these options and has the shortest bus journey. So personally i would still say Uckfield is the best choice by far.