The 747 is a slightly special case as there are "seeded" blind lines. Ie one long trip (the seed) and the rest are constructed by the company. At worst you'll do 5 trips but BA are pretty bad at constructing lines so probably less. My easiest month was 1 trip and then I did an overtime trip and I had a week's leave.
No one can show you an EASA roster as phase 1 bidding for Feb only closed this morning and Feb is the first month we'll be fully (haw haw) compliant with EASA. Most people on other fora are less than confident the show will stay on the road but that's another matter.