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63: Down to 5, right to 20, up to 25, right to 30, left to 38, up to 45, left to 48, up to 57, left to 63.

I've also got up to 65 on similar strategies, but that's the best one I've got written down.

I got 66 but I didn't track the steps. I'll try to get there again and document.

Diagonal moves by alternating directions are helpful.

69: Alternate down/right to 18, up/right to 30, up to 32, right, left to 40, up to 46, left to 49, up to 55, left/up to 65, left to 69.

71: same as above up to 55, then left to 60, up to 65 and right to 71.