Yes, but the inductor needs to be tuned and to minimize that 377Khz, the higher the Q the better.

Take a look at this data sheet:

https://katalog.we-online.de/pbs/datasheet/7447070.pdfNotice a sweet spot between 4&5MHz where the impedance reaches 3KOhm, yet, above 5Mhz the resistance drops.

The same thing counts for your current inductor with it's core. It's current highest impedance may already be tuned to 377KHz. An like this chart, if you increase the inductance, you may be improving/increasing resistance for say a 250Khz signal, but, at 377KHz, the resistance may begin to lower because 377KHz is now on the right hand side of that bump.

Like I said, did the manufacturers of that module choose the optimum inductor, or just pick something off the shelf to a close value?

Did you categorize that inductor knowing where that high impedance notch it located?

Is 377Khz centered in the middle of that high impedance tuned point?

Maybe the filter cap is the wrong value, you might just need a beefier lower ESR cap to fix the problem.

Here is another one:

https://media.digikey.com/pdf/Data%20Sheets/Wurth%20Electronics%20PDFs/S14100035.pdfNotice the attenuation in decibels has a unique sweet spot at 1.5MHz, and only 1.5MHz.

As you can guess, this inductor was designed to work well with a 1.5MHz calss D amp output filter.

A heavy capacitor on that inductor may drag down that 1.5Mhz, but it will begin to heat up.

Now, will changing the windings on your current inductors improve their notch if it already isn't at 377KHz, or, will it just muddy up it's Q? What's the best frequency for the core's of those inductors. The kind of look like almost identical to the one in the second datasheet here:

https://www.digikey.com/products/en?keywords=S14100035Could this mean the manufacturer use the wrong inductor, they used one designed for a 1.5MHz switching amp?

You said your source was 377KHz & 67v power source. In the datasheet for that inductor, there is an almost 20db drop at 400KHz. That leaves you with a 4v signal and an inductor which would get toasty with a parallel cap trying to short out that signal to an even lower voltage.

After all this, what I'm basically saying is if you cannot measure you current inductor's series impedance vs frequency, adding coil turns will be a shot in the dark.