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I'd recommend using 3Uw' Uw (R' F R F' R U' R') 3Uw Uw' instead. You can execute the 3Uw' Uw and 3Uw Uw' parts as a slice if you'd prefer. In general, R' F R F' R U' R' is a faster flipping alg since it's regripless and doesn't require rotations. (Some people also do the inverse: R U R' F R' F' R - I actually used to do this too but I find the alternative a bit quicker.)
BTW, even if it's not the fastest way to do it, congrats on finding your own alg! It's very satisfying when you understand cubes enough to come up with your own ways to solve things