I wouldn't be too worried about excess grease getting onto the brake discs. Yes, it's possible, but in practice it's really not very likely so long as you apply a modicum of common sense. In the fifteen years I've owned a Morgan, greasing every 1500 miles or so, I've never found any grease anywhere the discs, and I'm not the most particular about wiping off stray grease.
One tip that makes the whole process a bazillion times easier is to fit 60 degree angled grease nipples to the bottom fittings, with these fitted you can do the greasing without even jacking the car up - but of course it's a great deal easier if you get it up on axle stands.
Make sure you wipe around the grease nipple before applying the grease, and pump grease in until you can see grease starting to ooze out at the base of the main spring. A wipe around, a quick visual check of the other suspension components and you're done.
This is one of those jobs that can be done in less than ten minutes, but it's always best not to let on to SWMBO how quick and simple it is - that way you can be sure of a good hour or so's peace and quiet once in a while
