I was going to pick Arthur Gilligan over Fred Tate, but his Wikipedia and Cricinfo pages have him down as being born in London. Hopefully Fred and Maurice can cope with the temporal shenanigans needed for them to play together.
I think it's a general problem, that batsman are just unreliable...
I managed to remember:
1
2
3 Willie Quaife (played for Warwickshire when he played for England)
4 Alan Wells
5 James Langridge
6 Jim Parks (w)
7 Maurice Tate
8 Alan Oakman
9 Fred Tate
10 James Kirtley
11 Ed Giddins
I did dig out two openers by going through people on the Sussex top scorers...