The only advice I have is to try different tires to see if there's one that you can safely be run at the pressure you like, learn to live with a reduced pressure, or rebuild the wheels with hooked rims.

The OPs experience mirrors my own. Back when straight-sided rims were the norm there was no problem finding tires rated for over 100psi and they didn't suffer from such spontaneous blowouts even at 120 psi (which I used routinely on our tandem). But now that new rims are made with hooked sides the tire makers appear to have changed their tire designs slightly with the result that they no longer work reliably with straight-sided rims at pressures over about 80 psi.