Which, mind you, seems to have a bit of a reputation for being noisy with external mics. If the H2 is any indication, I can see why:
Avisoft Bioacoustics Hardware and software for investigating animal sound communication: ultrasound microphones, integrated acoustic data acquisition systems, recording and sound analysis software optimized for applications in bioacoustics.
avisoft.com
-99 dBu A-wtd / -95 dBu unwtd, yikes. That's like 10 µV. This makes a TL071 preamp on a 9 V cell look like the epitome of high fidelity. I haven't checked for the availability of small external mic preamps lately, one of those would be a good idea though.
When it comes to consumer-level/video microphones with plug-in power, there are two things that can ruin your day:
1. The input amplifiers themselves (and other misc. factors).
2. The bias voltage, as roughly half of any noise on there is going to end up in the input (depending on mic and its effective source impedance).
For example, Realtek onboard audio tends to have decent enough input stages but their insistence of generating mic bias voltage all internally leads to it being on the noisy side, resulting in consistently mediocre noise performance with electret mics. At the same time their input stages still are quite noisy by the standards of dynamic mics (I once got an estimate of ca. 20 nV/√(Hz), or ~2.8 µV of input noise in 20 kHz), so it's not an ideal experience for anyone. Now an XLR condenser mic with an external phantom power adapter, that should work decently assuming you can record L-R.
Looks like a Panasonic WM61-inspired capsule. Actually quite decent for noise by itself.
Max gain on the scaler seems to be +26.078 dB --> +52.156 dB total or ~400.
So you are seeing an input noise level of -97.91 dBFS rms on the ADC in this setup?
That would be
+20 dBV (= 10 Vrms) - 52,15 dB - 97,91 dB = -130.06 dBV = -127.85 dBu (shorted).
Assuming a 20 kHz bandwidth, that translates to 2.22 nV/√(Hz) worth of input noise density, which seems plausible given that the OPA1612 used in the scaler is spec'd at 1.1 nV/√(Hz) and you'd need super low resistor values to get particularly close to this. The Scaler's "Residual noise" spec of "250nVrms(A) @ 26db gain" suggests about 1.77 nV/√(Hz), but that's A-weighted and those values tend to be around 2 dB lower. If you add 2 dB you get almost exactly your results.
A little electret mic is not going to require input noise as low as this by any stretch as their FETs generate plenty of noise by themselves. Something around 10 nV/√(Hz) tends to be perfectly fine. Chances are you could get by just fine with just one section of the Scaler, especially if you were to reduce the ADC's input voltage range as well. Even in the 10 V range, your effective ADC noise floor would already be at <0.5 µV (or <3.5 nV/√(Hz)) like that, more than good enough.
Are you sure? +30 dBu would be about 24.5 Vrms, and the scaler doesn't go below unity gain.