Loriath, it's your trip so you should set the schedule however you want. I just thought you were trying to rank up exploring and not go on a tourist vacation. I think explorers normally go a little faster than that. They also try to find unexplored areas so they can get the 'discovered by' bonus. Also, so soon after 2.1 drops, I'd think people would want to get back to the game asap.
If was planing a trip (by myself), I'd head off at some odd angle until I found some unexplored space, then turn for the core. I'd probably travel about 4000LY a day, which would take about 2 hours. I'd also explore profitable systems about another 2 hours. I'd probably spend a little more time on the weekend and I'd be there in a week, and back a week later. But I've traveled over 350,000LY, so I'm an old hand at exploration.
Now if I wanted to be part of a group, I could see taking a more leisurely pace. 2000LY a day is only 1 hour a day travel time for those that don't have a lot of time, and that would take about 2 weeks. Then you can pad that as much as you want with exploring systems and a few meetups (and Netflix). I'd also stay away from tourist attractions like nebulae because the space around them will be explored to death.
Anyway, that's my 2-cents. I may feel a little differently about a longer trip next month.
PS. I've heard only great things about Discord, although I haven't tried it myself. It looks 1000 times better than Skype at any rate.