You can definitely do it either way, many people are doing all 3 mesos twice through in the manner you did meso1, some are just doing 1 or 2 of the mesocycles twice through. I'm not sure there is a better way, it's more of a preference. I'm kind of impatient, so I've been doing these all one time through, I'll finish up meso2 this week.
I think that Cathe said she'd originally conceived of STS being done that way (where each meso takes 8 weeks) but felt that many people wouldn't want to commit to a 6 month rotation. So you shouldn't hesitate to keep doing the rest of STS the way you've done it so far.
I don't know which is best, but I'm doing the 6 month and am in week 1 of Meso 2. I plan to do each week twice as I did for Meso 1. For me, the second time I do a workout is always more effective and I think it helps before I move on to the next week. Part of it may be mental preparation but whatever it is, it's more effective and I feel I can push myself more.