WWP - Welcome!
I have a D90, which I understand has more or less the same high ISO performance as your D300. To me, it's a no-brainer: crank up the ISO.
As long as the shot is properly exposed, the noise from high ISO should be much less than you probably would expect. I'd bet that an ISO of 3200 wouldn't produce much noise during a daytime shot; and if it did, then it should be a pretty easy fix with a noise reduction program.
Just as a reference (not a great shot by any means), here's one I took at night with a 70-300mm VR, ISO 6400, f/5.6 and shutter of 1/200th. No noise reduction has been done to it. If my D90 can do this decent of job at a night high school football game, I'd bet that your D300 can do a better job at f/6.3 on a cloudy afternoon.
You've got a D300 with a great CMOS sensor - use it!
