I'd highly recommend just selling the F3 and getting a tascam FR-AV2 if you want to use PIP mics on a device with this form factor. Fewer adapters means fewer places for things to go wrong, and the Tascam is an excellent device.
Fwiw, I use the LOM Phantom Adapter with the Zoom F3 and it's excellent. On the XLR end, you can't tug it free by design, and on the 3.5mm end, you actually have a really nice, secure connection that is hard to disconnect by accident (I'd say harder than on most recorders).
The one caveat about the LOM offering is that it adds a lot of gain (this is an undocumented feature) - it essentially works as a +16db preamp. It's very clean gain that won't increase your noise floor at all, but I'd be wary about using it with very sensitive mics and loud sources. With a pair of CA-11s, I've had no issues at all.