It doesn't solve the clipping problem, in fact makes it worse (get a leaf sweeper and pile grass clippings by the back fence), but if you don't have a huge lawn and have lots of time, a European scythe is a great way to cut grass. No grass too high for it, either.
Just an alternative if you're getting a new mower. I cut an acre but I have _lots_ of time. You do a few swaths a day and by the time you get done with the whole lawn, it's a perfect time to repeat, at that size.
A scythe leaves a windrow of clippings at the edge of every ten-foot-wide pass though, indeed that's its original point.
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has a nice outfit, you need snath (I suggest straight, which works best with long grass blades), blade (26" grass is good general one; the 36" is good on easier spring grass), sharpening stone (Begrenzer medium grit is good), bar peen hammer and wide anvil (for thinning the edge again after you've sharpened it away enough); and stone-holder, since you stop and sharpen every 5 minutes or so, for a few sharpening strokes. A lot of stuff but a nice pasttime. They have a package deal on price, the last I looked.
With a European scythe, you're slicing grass, not whacking it. It's a very smooth activity. The blade rides flat on the ground, the curve of the back keeping the edge just off the ground, and the odd shape of the snath that holds it is to keep that geometry through the stroke.