1. Amplifier noise

2. Noise greater than the Nyquist frequency will alias (FNyquist = 125kHz)
Each 125kHz frequency subinterval will fold back onto the Nyquist band. The total noise will add as the square root the sum of the squares as the noise is random and uncorrelated.

3. Estimate total aliased noise seen by ADC using Excel
entot ≈ 50nV/rtHz
entot ≈ 650nV/rtHz
Your measured data
entot ≈ 40nV/rtHz
entot ≈ 225nV/rtHz
Estimate from excel
The above estimate from excel shows what would happen of we alias all frequency subintervals from 125kHz to 10MHz. The excel noise estimate would increase further if we go beyond 10MHz but the value approaches a constant value. The broadband estimate is close to the measured results (40 vs 50). The measured 1/f noise region is larger than expected (650 vs 225). This may in part be due to process variation. 1/f noise is especially sensitive to 1/f variation. The discrepancy may also be temperature drift that is interpreted as 1/f noise.

4. How to improve this?
I think the main issue you are having with noise is the 1/f region. Since you are planning on using a digital filter to limit the bandwidth (and noise) to 200Hz, so you want minimal 1/f noise. Also, an antialiasing filter that can limit the bandwidth (and amplifier output noise) to less than 125kHz will prevent noise fold-back.
We will put together a proposal that should improve this. The noise density curve shown here is an option we will investigate (OPA188). It doesn’t have 1/f noise as it is a chopper amplifier.