"In the interest of time, I would like to clarify a few points/things first." This is the most polite way to say it. The other way is fine too, but it might sound rude, presumptive, or 'short' to some people...in America at least. 'Spare us both the time' might be interpreted that you don't value this project highly or that you think too highly of yourself and your time. Further, it may imply that the other person is at fault for having laid out an unclear, not well thought out plan that is now wasting 'your precious time.'

Those are correct. More formal would be: “let’s spare both of us our time”