RPM for a 22" residential push mower

[jekjr]

I know that the blade tip speed is limited by ANSI to 19000 FPM. Which, on a 22" blade, equates to 3299RPM according to my calculator. I recently bought a tachometer, and found that my residential push mower, with a 22" blade, is running at 2750 RPM. So I started increasing it. When I got to 2950, it seemed like it was running really fast, and had a lot of vibration. So I backed it down to 2900, and the vibrations seem to get better. So my question is, of course, what speed should I set my engine to?

Engine: Briggs 128T05-5123-B.
Mower: 2011 Toro Recycler w/Personal Pace.

I still have the owner's manual and the engine manual. Neither mention engine RPM settings.

Not sure if this is the right forum, but the only other blade tip speed discussion I could find was in this forum.

I see this discussion in numerous places. I am retired now but ran a lawn service for years. We ran Scag Tiger Cat mowers with Kawasaki engines on them primarily. When I stared cutting back on my business a few years before I completely retired I had four. I always had them set up to run 3600 RPM. I have seen them run 3500 hours plus and still be going strong running at that RPM. Set up correctly they would cut 14 day Bahia Grass all day long week in and week out. Over the years I noticed a few RPM drop would change the cut quality severely. I understand there is much debate on it but 99% of those who say differently never cut 14 day Bahia Grass.