Resolving NIntegrate and NSum non-numeric evaluation errors in oscillatory integrands

I’m working on a Mathematica code that involves nested NIntegrate and NSum with oscillatory integrands, but I’m encountering several non-numeric evaluation errors. The relevant part of the code is below:

When I run this, I get errors like:

Power::infy: Infinite expression 1/0 encountered.
NIntegrate::inumr: The integrand has evaluated to non-numerical values for all sampling points.
NSum::nsnum: Summand is not numerical at point m = 100.