I was also a bit worried about grinding for 8 characters, but today, I did all the H2+ except 3 and I went from influence 2-3 to influence 10 with the four alliance specialists.
If it was legacy bound, you'll just have to do that 3-4 times to get maxed, so 3-4 afternoon. And after that, what ? A whole part of the 4.0 system just finished and not much to do...Btw, it's pretty easy to up the companions influence : doing all H2+ gives you 60 crates, so a lot of gifts too.
But I won't lie, it was hardcore grinding, running from a place to another for...5 hours perhaps ?