I usually use a Zoom F3 paired with CA-11 cards, and after running some tests, I found that the microphones are the bottleneck in terms of self-noise. Whether I plug them straight into the F3 (with a battery box + adapter) or add a pre-amp to the chain with a lot more clean gain, the level difference between a test signal and the gear's self-noise remains the same.
I also ran the same test with a pair of Clippys, which are way more sensitive and have less self-noise than the CA-11s. With Clippys>Battery box>Adapter>F3, the difference between the test signal and the gear's self noise was about 4dB greater than the result I got with the CA-11s>Battery box>Adapter>F3 rig - that is, changing the mics increased the signal to noise ratio by 4dB. With the Clippys>Pre-amp>Adapter>F3 rig, the difference was 5dB. This means that adding loads of gain between the Clippys and the Zoom F3 only increased the signal to noise ratio by 1dB.
My conclusion is that unless your microphones have EXTREMELY low self-noise, it's pointless to worry about the Zoom F3's gain staging.