All 16 companies will be involved in the overtime bans on those days.
It would be hoped that individual trains affected would be updated on the Journey Check pages of the relevant train companies by 10pm the previous night. But you need to be able to be nimble. In my part of the world, Northern Rail, on such days we get cancellations (and sometimes reinstated trains) happening at very short notice through the day. I have had trains cancelled after they were meant to depart on such days.
It really is a case of being flexible and patient. If a train is cancelled by 10pm there is no delay repay compensation, after 10pm normal rules apply. So a 1 hour delay gives you a 100% refund.
There is only one bus a day from Salisbury to London.
What happens on South Western is that many Salisbury to Waterloo trains run through from Exeter. On days such as that the service is often split at Salisbury- so Exeter to Salisbury is vulnerable, Salisbury to Waterloo is more resilient.
And there are so many trains London to Gatwick that is not an issue, as long as you get there before the evening commuter peak.
Salisbury to Winchester there is a Citybus #68 at 1000, returning at 1440 and 1638.
