You'd probably have to spend a fair bit of money to get something substantially better than the Squier VM you've already got; it's a really good bass that sounds great for what you paid for it. The player will be better, but not another $700 better, IMO.
I also strongly recommend against upgrading or modding any bass, including yours. I won't go into all the details of why, I'll just say that at the end of the day, the bang/buck ratio of an upgrade is nearly always significantly lower than simply selling and getting another bass that's more along the lines of what you want.
So my personal recommendation is to only spend money for a really substantial upgrade. That's just been my experience over the years trying the "incremental" least-expensive route into a better instrument. That's always, and I mean always, more expensive than just jumping to the more suitable/desirable bass from the get-go.
If so, my recommendations for a largest possible jump in quality for more or less the least amount of money for an FL are (in order of recommendation):
- Carvin/Kiesel Brian Bromberg sig. If I were gigging and I mean just wearing it out both on the strap or seated, all night every night, the Kiesel B24 FL would be my first choice. Options would be radiused humbucker pickups and unlined FL neck. This is the most ergonomic bass ever designed and your arms and hands would thank you for going this route. Drawbacks are expensive, hard to find used (because it's kind of a poor seller), and takes forever to get one.
- G&L L2000 with unlined jazz dimensioned neck. This is the G&L L2000 experience, the only drawback being takes forever to either find or order an unlined FL version.
- Fender Tony Franklin. This is basically a 70's Fender P/J with an unlined ebony board and a PU switch. This one is basically the Fender Precision experience, with all those pros and cons.
- Fender American Professional FL. This is the Fender JB FL experience, which you're already familiar with more or less.
And maybe a few others, but this is the least amount of quality I'd actually spend money to replace your present bass. If not, I'd just keep on with your VM for now.
And of course, far better if you can find any of these used, of course.
L