Pipe length depends on the exact speed you want the tuned exhaust to kick in. I think most people doing home-tuning either begin with a trombone set-up until they find the right length, or keep cutting or extending the first section of pipe until they like what they get. I can't see much point in what you are aiming to do. You could improve the power output in a specific speed band, and rotary mowers normally work in a rather narrow speed band, so that makes sense, but you could achieve more by putting a larger engine on the mower. Remember, you'll end up with the engine wrapped up in pipe like a ball of wool, with a long expansion box sticking up in your face. You can't baffle the expansion box at all, so you'll have a head-full of noise and fumes like riding an old-time speedway bike. (Add a little Castrol-R to the fuel and you'll complete the feeling.)
