I'm about 9 months in to a year-long trip and loving it (you can check out my travel blog at scottandnina.com if you're interested). We're both in our early 30s. The advantages and disadvantages you've laid out sound spot on. For me, last year I finished my pediatrics residency and my husband was trying his hand at writing, so it was easy enough to have a clear starting point for our trip. We haven't started the job search in earnest yet, but I'm under the (hopefully not mistaken) impression that I shouldn't have too much trouble finding a job as a general pediatrician, especially since I'm flexible on location. My husband has been involved in several different fields and was actually offered a job out of the blue while we were on our trip that combined two of his disparate fields. We considered it for a while, but it would have meant cutting our trip short, and in the end we decided to pass up the tempting paycheck (hopefully not a bad decision!). When we get back, we're planning on working hard for the next few years to reach semi-FI/FI soon and then take another trip.
I've been really happy with my decision to take the trip when we have. I suppose it would have been easier to just take a job out of residency and then fully retire and take a trip, but I was pretty burned out after residency and this trip has brought much-needed clarity of mind and value to my life. I've had some really cool experiences, read a ton of books, become vegetarian, and I'm currently learning Italian. It's been totally worth it to me, and I feel ready to go back to work after this.
Not to sound too morbid, but as a pediatrician I've seen kids die from cancer, car accidents, and weird freakish things. We have family dealing with chronic illness that keeps them at home. Part of the reason for doing this now was the "you never know what's going to happen later" that will derail you from your current plans. I feel like we're young enough that it's just not a big deal to have FI/semi-FI in flux and go back to work or get side jobs or part-time work if need be. It's too easy to focus on retiring at 35 or whatever, and calculate SWR based on conservative estimates and no income for the rest of your life and decide that you need a huge amount of money before you retire. I think what's worse is to keep putting off a dream, but in the end you have to decide how much that dream is worth to you. I guess you could also argue, though, that if the dream is important enough, you'll definitely make it happen and what's a few years? We wanted to do this while we were still young so we could hike the Annapurna Circuit in Nepal and the Routeburn Track in New Zealand and before we had kids that could make everything a lot more complicated.
I think from the financially "sensible" perspective, you should wait. But it's really up to you whether the financial cost is worth it to you (personally, it was to me). Good luck with your decision and honestly, I think you'll probably end up happy with either choice. Do you think you'll regret going on your trip after the fact? Will you regret going down the other path and being financially independent earlier? I think a lot also depends on what sort of field you're in and what your job market is like and how much you like your job.