I'm not on absolutely steady ground here but we'll have a go.

You appear to have a pre-modded PS2.

Your PAL/60 game - well, that'll teach you to NOT get a backup made in Botswana! So, first, try this link ####://retro.co.za/tv/

I don't think there are any published patches but someone had to have had one to make that backup in the first place. If that patch could be found, it could be reveresd.

Then consider having the signal come out as pure AV. For this you would need a fully loaded Scart lead (not the one that comes with the PS2). In the UK this is sold as the BLAZE Scart Lead. That should provide the syncronisation because it works for 60Hz NTSC.