When I asked, the 4090 grid was not available. Doesn't hurt to ask again, though. If you get a different answer please let me know.
DIY APEs will boot the high mid / low treble more, so that's probably not what you want.. and yes, they also change the polar pattern, making them more directional as the frequency goes up and less perfectly omnidirectinal, but that and the presence boot is the whole point of using them.
I'm no acoustician, and hopefully someone will confim or correct what this, but as I understand it the tube acts as a resonant chamber, with the frequency of that resonance determined by the length and diameter of the tube. I think it's the 1/4 wavelength where the boost begins to become significant, the boost is reduced as the wave starts to to cancel at 1/2 wavelength, then reinforces again at 1 wavelength, etc. In practical terms, the shorter the grid, the higher frequency at which the onset of that frequency boost sequence starts and the less apparent it will sound. I suspect the grid on the 4090 (which may be permanently attached) is shorter than the 4060 soft boost grid, but I don't know by how much. I've considered trimming some high boost grids which I never use down to something shorter than the low boost grids, or making shorter ones of various length out of plastic or brass tubing of the same diameter, but haven't done that. It would require careful test measurements in comparision with the standard grid to figure out how exactly the response is being changed.. or lots of careful listening to dial it in by ear to something that sounds like the target response you prefer- tricky or a good bit of work.
The easier answer and the reason I've never done any of that is to simply apply corrective EQ. I prefer using the low boost grids and making an EQ adjustment later anyway, since I can then alter the shape of the EQ curve as required for each particular recording and they are all somewhat different. So I'm usually going to EQ in any case, and even if I'm reducing the grid induced boost with EQ to something that is the equivalent of flat or rolled off, the grid's high frequency boost is still useful as 'pre-emphasis', effectively lowering the apparent self noise of the microphone since the self noise in that region is also reduced when the correction is applied. That can be very helpful for clasical recording with the 4060 even though it is relatively quiet for a mic with a such a tiny diaphram.
[edit- BTW, welcome to the forum!]