First babies do drop earlier, and once they're engaged in the pelvis, that's usually it.
OTOH... first babies also sometimes stay breech longer. The usual "rule" is if it's still breech at 37, it's not likely to move because it's run out of room. But a good number of babies flip at 35-36. At 37, you start making decisions. An elective CS is scheduled at 39 or a little after (some docs will schedule on your EDD; it really depends on how the calendar works out). Frankly, if the baby's breech and engaged at 39 weeks, your chances of having it move are slim to none, so you're not losing any time in that sense.
Anecdata: First baby stayed high and breech till 36 weeks, when she flipped and engaged. 2nd baby, in my nice stretched out uterus, went vertex months ago and is busy hanging out at the bottom.
A version is a good option if your doc is experienced. With an experienced OB and proper precautions, ECV is safe and has a good success rate (keep in mind that some babies won't turn for a good reason). My first hospital (on the NHS) prided itself on having a 100% ECV offer rate and something like 75% of ECVs worked. If the baby doesn't appear to like the ECV, they'll stop. It is uncomfortable, and it needs to be done in the hospital, but if you're a good candidate it's seriously worth considering. People will recommend trying things like chiro and moxibustion, but ECV has the most solid evidence backing its use. Also, I've heard people say things like "you need to use moxibustion early to make it work".... well, that will mush in the natural likelihood of the baby to turn on its own with anything the technique itself did. (Yes, I'm aware of that study that claimed an 82% success rate with the Webster Technique: there are some huge flaws with that study.)
Breech vaginal delivery? Well, you need a doc/MW who has attended a lot of breech births and knows what to do. The chances of your OB being one of them? Slim to none. There are fewer and fewer practitioners who know how to attend breech birth, and this was true even before the Term Breech Trial. That was the death blow, but things were already shaky. I have my doubts as to whether we'll ever really see a swing back because it's so hard for doctors to get the experience that makes vaginal breech safe. If you happen to have a local OB/MW with a good reputation for breech (and I mean good in all senses: I do occasionally hear about providers who slip over the line into "cavalier"), and you're willing to switch at this point, then you might consider it. But this may really not be practical advice for many women, and it's far from unreasonable to schedule a CS if it comes to that. It's what I would have done had my DD not flipped (she wound up needing a CS anyway for entirely different reasons). I could've showed up and refused a section, but honestly, I figured that a CS was safer than a vaginal birth with midwives and OBs who had never voluntarily attended one.