I am not familiar with the technical side if this exact issue (PS2 not reading DVDs recorded at 4x) but here's a guess... something I would try. BenQ is a good-quality writer at 4x, or any speed for that matter, but the reason the PS2 drive is not reading the DVDs recorded by BenQ could be related to the way WOPC (optimal power control) works during recording. It interrupts writing, and that typically leads to PIF errors at relink points where writing restarts. (It's hard for the drive to resume recording on a disc rotating at several thousand RPM within a few microns of the point where recording stopped at a recalibration point.)
If you use B7U9 firmware and disable WOPC using QSuite, that should get rid of some potentially significant PIF errors caused by OPC operation. If my guess is right and PS2 DVD-ROM drive is overly sensitive to relink points, it may help.
I recommend YUDEN000T02 or TYG02 media for this experiment. It works very well with WOPC disabled.
As a rule, lowering recording speed on BenQ 1620 below rated speed of the media doesn't improve quality.
Post a quality scan of one of the discs that PS2 reads, and one that fails. There may be some clues there.