Interesting intent to change the cap. For my understanding especially the softer wood is the reason of these phones extraordinary contoured bass. Softer wood - better slow frequency response.
A classic violin is made of different woods. Maple chassis for stability, but spruce for upper shell, bass bar and sound post. And there‘s ebony as neck, fingerboard and nut/peg box. The denser, harder wood is good for its high frequency resonance, but the spruce gives the sound contour, its body. Spruce is for my understanding not the most tolerant thing in fast drying processes. The not to distantly related pine is more… stoic with that. Especially in thinner cuts. I was surprised when Grado released 2 Heritage models in September ‘18, both made of the same wood. But they sounded different. I guess the more every day suitable highs resulted in the S Cushions. Of which I am not the biggest fan. But there was also something in the lows and lower mids where these phones are different. On first impression the GH4 appeared to have the bigger punch. Bigger, but not harder. I felt the GH3 have more texture there. Speaking of thinner cuts, I think this is one result of this cut and the lower mass of soft wood. As if John Grado found 2 appealing soundings while experimenting with the draft samples of the new softer wood.
Normally with wood a softer glue is used (by carpenters, joiners) because a more elastic compound is needed. So my idea would be to use the tip of a triangle blade crafting knife. My colleagues in the US (back in the days) called these X-acto(?). Like it more than heating up a mylar membrane. I would cut/scrape the wasted glue, then stick the tip carefully into the glue, move the handle slightly center, outwards, center, outwards, and so on. Not to deep, not back and forth. Might cut the cup. Then the next millimeter …clockwise. If I remember right the drivers lower housing wall is about 6, 7 mm deep glued. It might take 7 rounds.
slowly but surely …
(More effective ideas are always welcome)
I am extremely curious to see the result of your modding idea.