As stated the problem is the stiffer springs, to give 'sportier' handling. It might give some improvement on a motorway and will be less of an issue on smooth roads.
Back in the last century it was common for recommended tyre pressures to be in the upper 20's psi
sometimes with the option to raise this for 'high speeds ' or a heavy load.
I dont think tyre technology has changed that much. Todays higher pressures are primarily to improve fuel consumption . Sometimes suspension design is tuned to improve ride at this pressure, but maybe not with 'sports' suspension.
I am reluctant to suggest trying a lower pressure , as there may be safety issues, or higher fuel consumption. You could argue that many people neglect to check their tyre pressures anyway which naturally drop due to cold weather, natural permeation through rubber, punctures leaks etc, .They will often be inadvertently running well below recommended pressure for most of their miles. Usually without serious issues apart from increased fuel consumption.
But if you do experiment and try a slightly lower pressure its probably a good idea to ensure you check your tyre pressures , and tyre condition, more often than before. If you start off with lower pressures they could reach dangerously low pressures that much sooner.
If you do find a lower pressure is satisfactory for local trips maybe increase the pressures again for a long, fast ,motorway trip.