As I read the letter if you break your contract by not turning up for a trip (and I believe that during industrial dispute the rosters will be torn up, you'll get minimum notice for whatever trip BA decides to operate and you'll be expected to show) then you are going to be permanantly losing staff travel. If you are sick you are going to have to prove that you are sick. The 7 day rule for doctors notices won't apply and if you think it does its going to take some very expensive weeks in court to decide if you are correct. If you are down route it is normal practice to work your trip home. Expect the company to askyou before hand if you are going to back BA. If you say no then BA will apply the same sanctions to you. If you say yes then expect to get minimum legal rest back in the UK then another trip out. You can't hide on this one. If you vote for a strike then realise that is exactly what you'll get and you will be declaring to BA whether or not you are in or out.
Good luck with the ballot. I hope that you realise just where BASSA reps are taking you.