Can't be arsed to re-read all this so apologies if duplicated info, but I've just wandered past Burgess Hill station and it appears that roughly 2 out of 3 southbound services are cancelled, so don't assume that because you're boarding south of Haywards Heath you won't have a problem.
If they're reporting bricks on the line, it rather suggests the whole tunnel will need properly surveying and repairing (with the necessary shoring up/scaffolding etc).
I'm no building expert but that doesn't sound like the sort of problem you can fix in a day or two. More like weeks???
The...
From Southern Rail Twitter feed:
NR have informed us that line btwn HHE & TBD will be closed all day. FCC, SWT & SET accepting our tickets on all reasonable routes