Full range sweep - odd graph

The slope looks to me like there's a 6 dB/octave high pass filter with -3 dB at somewhere around 6-7 kHz.
This is a first-order filter, i.e. probably a normal RC high pass filter.

My guess is you have a significant impedance mismatch of some sort in the signal chain, and capacitor-coupled outputs.

Consider:
f = 1 / (2 pi R C)

Where R is roughly equal to the input impedance, and C is the output capacitor.
Assume perhaps a cutoff frequency intended at 20 Hz, and we'll have a mismatch of about 300x.
Pro XLR is 600 ohm, and consumer RCA usually 10k-20k ohm so this is 10x higher than you'd expect. Odd indeed.

I looked up the specifics on your gear.

Well, yes and no.
An unbalanced (like mono headphone plug) 1/4" to RCA converter should work for you, with some caveats...

TRS signal levels are higher than RCA, but since you have an adjustable limiter on the amp you can set it to not overpower the input.

Low-impedance (XLR/TRS) output into high-impedance (RCA) input shouldn't cause this as such, it should cause the opposite, no blocking of infrasound.
The other way around, high into low would cause something like this slope, but generally up to more like 600 Hz than 6000...

So yes, the culprit is most likely the XLR converter.
Without a power supply, there's no elegant way to convert between XLR and RCA that works with every type of gear.
Simply taking the positive pin as signal and grounding the negative side would work fine on some gear and damage others. This would be "unbalanced XLR".
(It would work fine on your amp according to the data sheet.)

In this case I think your converter might be using a transformer, which is impossible to get right with unknown variables... but it is less likely to damage the gear.
If it is creating a series-resonant bandpass filter (R L C in series), it would also drop off at 6 dB/oct after the peak, and it looks like that could be what's happening. Your microphone is supposed to be flat to 20 kHz, and 7kHz seems early for speakers to start rolling off. (Decent trebles are fairly cheap.)