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You shouldn't need those two screws that hold the bridge on. To lower the action, yeah - adjust the saddle height (but keep an eye on what happens to the action / buzzing at the nut end as you do it). I think you'll then have intonation to redo.
I'm no expert at this, but I think if you do a couple of rounds of saddle height / intonation then you'll get somewhere close. If you start getting buzz at the nut end, that's when I'd take it for a real set up.
Edit: if you're really adventurous you can shim the heel, which will shift the angle of the neck by a nudge - Fender certainly used to do this back in the day to get action decent at both ends of the neck.
What do the two screws on the bridge do? Is there any adjustment there or do they just hold the bridge onto the body?