Nope, no worky. But the concept seems easy to visualize and should work well. I have an actual manufactured "Spindle-Luber" that were common in the magazines and 4wd shops in the late-'80's. Got one each for the 44 and the 60.
If your spindles are off though joel, then what ransil said. I've used carb-cleaner spray to good effect. If you've got grit in there you definitely want to clean them out good and deep. The rollers are pretty well captured, so you can get in there with your fingers, rags, sprays and brushes, or whatever else you have laying around, and clean them out good.
Then you just pack them like you would any bearing. Work the grease in there by finger tip until it's literally squeezing out of every gap and you can't force any more in there.
Once that's done, a common practice is to pack up a goodly amount of grease into the spindle bore itself. Seems counter-productive, but what happens is that the axle shaft just pushes the excess out into your hand (hopefully!) when you install the spindle. Assuming the spindle's bore is clean (and it should be by now), you can simply take that excess grease and use it to pack your wheel bearings.
What this does is to fill the cavity between the spindle wall and the axle shaft, and keeps water intrusion to an absolute minimum. Any that gets by the seals is slowed down even more by the grease.
I'd use the same grease that you're going to do the wheel bearings with obviously, but try to use the most water resistant and/or high-temp grease you can find. A marine grade bearing grease might be worthwhile to look at, if it has the proper specs for wheel bearings. I've just used whatever high-end synthetic or semi-synthetic grease was at my local parts store, but I've always used what I thought might be the better stuff, even if it was more expensive.
It's just cheap insurance...
Paul