I've been sitting here thinking about this problem for more than half an hour now. ( and now more than an hour as I type in this response! )
At first, I thought you were making an unwarranted assumption: that a complicated nonlinear system of transmission and absorption spectra curves could be summarized into a single correction factor.
But the more I think about it, the more I think that to a 1st order approximation, there should be a single linear correction factor that might be good enough for what you are trying to do. I don't think knowing the transmission spectrum of pyrocat stain will get you there though, there are too many other factors that matter ( spectrum of source light, transmission of glass in your contact frame if you use one, and most importantly transmission and depth of penetration of actinic light in the surface of your Pd paper )
But consider this:
When a photon hits your Pd paper, it takes a certain quantum of energy to convert Fe3 to Fe2 and initiate the reaction ( call it the equivalent of an X nm photon). The rest of the energy is released as heat. For this to happen, the photon does not need to have exact X nm energy, it just needs to have at least that much. So we don't want to think about how many X nm photons there are, but how many that are shorter wavelength than X.
The same thing is true of the UV LED that you are using as a sensor... it will absorb the amount of energy equivalent to a 395 nm photon, and release the rest as heat.
Also, imagine a transmission curve ( in units of W/surface area ) with higher energy shorter wavelength photons on the left and lower energy longer wavelength light to the right. On the left side there is going to be something like a hard cutoff, with very little UVB getting through the contact frame glass ( or though the glass of the UV tube for that matter ). So if you integrate the area under the curve from that point up to the "X" energy needed to convert Fe3 to Fe2, that's the energy density of actinic light. ( It also means we don't need to worry about higher energy photons... there aren't any gamma rays here that could scatter and produce secondary lower energy but still actinic photons.. we can assume that if an Fe3 is converted to Fe2, the photon that did it is now just heat )
No matter how complicated all those curves are, or how many different transmission curves combine to form the one that matters, as long as the spectrum of the source stays pretty constant, then the ratio of the total actinic energy density to your measured value with your UV LED should stay roughly constant. So it really would work to compute a single correction factor, although I think you're going to need to find that value empirically rather than try to guess it from the pyrocat stain properties. So as a crude measure of actinic energy density, I think you're okay.
But there's a pretty big flaw in all this logic. If the plastic dome on your UV LED sensor has a different hard cutoff from the print frame glass + paper surface, then it might not integrate over the entire spectrum that matters..... and even if it does, there's another more serious problem. The transmission spectrum of your negative is going to be nonlinear ( whether it's pyro or anything else ), as is the absorption spectrum of you Pd paper ( with self-masking and everything else ). The full spectrum of actinic light will react with Fe3 that's right on the surface of the paper, but as soon as the light needs to go any depth at all, the shorter wavelengths will fall off faster ( longer wavelengths are more penetrating ), so the spectrum that matters becomes more and more compressed ( to the area in the spectrum just below X ) for light that needs to penetrate the surface or go through density that has already been produced on your print. So I think this is going to be a problem... a single linear correction factor will correctly estimate the actinic UV that initially reaches the surface of the paper, but after that the relationship between your measured value and the compressed spectrum of actinic UV that will create further density on your print is nonlinear and could be very complicated.
I think what that translates to in terms of printing is that everything is going to work okay for the initial part of the exposure, but the Pd contrast curve will be different with the two different UV sources, and that's nonlinear and can't be estimated with a single number. So if you were printing a step wedge, it might be that a single conversion factor would work really well in the highlights, but not very well in the shadows. I think this is going to be true no matter what measuring device you use, because the thing that's driving it most is that a UV tube has a different spectrum than a UV LED, and that matters in a complicated way to the densities on your print. The same negative is not going to print the same with the two different sources, and it's not a linear relationship, so even if you have a good correction factor, you're still going to need to re-calibrate your process to account for this.
I guess the good news is that you still should be able to use your UV LED exposure meter, and you can probably very quickly get in the "right ballpark" with a couple tests. After that you'll probably need to re-calibrate your process to get the contrast and range of densities you want, and that's going to be true no matter what method you use to measure the UV.
Good luck and have fun!
