For instance, do you do the bonus jump on the first board, or try for a better time?
I go for the bonus jump (the one on the left). I usually finish with 53 or 54 seconds if I don't fall off, and I don't think you can clear it much quicker than that taking the regular path. Plus, you get at least 3500 for landing on the number grid.
And, is it possible to pull some of those tricks where your marble jumps to paths it normally can't get to? I have never been able to get to any real time saving areas.
It's possible to get on top of the maze on the Intermediate race, although I'm not good at doing it, so I don't usually try it. The good players usually do it though. The shortcut on the Silly Race (near the end) is also possible and I've done it a couple times. I don't know if any of the other short cuts on that video actually work though. That's a tool-assisted video from the Genesis version of Marble Madness, not the arcade.
Is there a way to get past the Hammers at the end of Race 4 cleanly? They always screw me up in a big way.
It depends on which arrangement you get. The ones that come out one at a time (1, 2, 3, 4). There's also single ones that come out in sort of random order (not really random, sorta like 1, 3, 4, 2, maybe not that exact sequence, I can't remember), those are easy. There's also all 4 at once, and 1 and 3, then 2 and 4, then all 4. The only one I find the hardest are the first one I described, that come out in sequence one at a time.
I don't think I've ever finished it by myself (I could do it when I played doubles with my brother, but I'd get an extra 5 seconds for each race I beat him on

) I've come really close several times though, at the last set of disappearing floors on the Ultimate Race. I normally get 50-60K.
Now I wish I had a machine of my own to play on

Last couple machines I played on were on vacation (Funspot in NH and Barcade in NYC)