Long term I don't know how the Sussex region will cope, as the problem really goes back to the LBSCR who built the lines so poorly.
There aren't really any hard rocks in South East or Central Southern England, so both LBSCR and South Eastern Railway often used ash mixture as lower ballast.
It was only in Southern Railway days that more suitable material (generally from Meldon Quarry, Dartmoor) became common.
Cannot just keep tipping ballast as track level would go up and eventually trains hit bridges, signals etc or platforms become too low etc.
There are only two ways to make long term repair, lift track, dig out ballast, dig out foundation layer to deeper depth, replace the old ballast in deeper hole as foundation (often with geo textile mats), replace track and new clean ballast on top. Time consuming and need to take away the lower clay/mud rubbish that is dug out.
The alternative is undercutting, a derivative of mining equipment, dig a hole at side and insert what looks like a horizontal chain bucket cutter, this then cuts and lifts out via conveyor at side, effectively get a slice out of the foundations so everything then drops into new hole, can then drop new ballast, lift track and tamp and align. Once started this is easy to do longer sections, but problem is can't use the machine where cables, drains or underbridge structures exist.
Some people get confused because they think the problem starts with the track or ballast, but Soil Moisture Deficit affects what is below the ballast, and if that moves around (heaves) then ballast and track above can also move. So only solution is to have deeper ballast (where stones interlock), or to cast a slab on something secure like piles