There's only one thing that I've seen anyone say that will kill the eggs, petroleum oil. All Seasons Spray Oil (98% petroleum oil) is one you can get at Home Depot for $13. I can't confirm it works or that it's safe to use around buds, just read about it in another thread.
I'm in an area where mites, thrips, and aphids are bad. It's because of the low humidity, around an average of 20%. I just got rid of thrips last night. Today I added two 10.0 UVB 18" fluoros to the grow room to help keep them away (they don't like UV). And tommorow, after doing a bit more research to find out what to feed them, I'll be getting Lady Bugs. Since Lady Bugs eat them I can't think of a better prevention.
If you have a grow room that is sealed off from the rest of the house, you might want to consider getting some to get rid of your mites. Home Depot sells them for $25 a pint, I imagine that's all you'll need. Just find out what they eat and pick some up so after the mites are gone you can keep them alive while you wait for the eggs to hatch so they can eat them too. That would be the safest way for your buds.
If you can't use Lady Bugs then I would recommend Mite X. You can find it at your nursery for $8.99. It's organic and safe to use up until you harvest, and it has Molasses & Sucrose which is good for the taste of your buds. Make sure to spray under the leaves and to get rid of the eggs after you kill them. You want to do it at the begining of a dark period because it's an oil, just keep some oscilating fans on your plants full blast and you shouldn't have to worry about mold/mildew. As soon as the lights come on, get rid of those eggs, or treat again in 7 days, then again 7 days later. It's up to you.