I'm now in my 4th year of water glassing. I've never had an egg break that badly, but my first two years, I did have eggs what cracked and leaked egg whites into the water. I didn't find out about that until I started using the eggs and saw a mess in that area of the bucket. Although the water and some of the surrounding shells were messy, it had no effect on the usability of the other eggs.
That said, it sounds like you had a worse leak than mine. I'm not worried about it in the short-term, but it might cause problems, particularly if the egg contents are exposed to air. My recommendation for this batch: carefully pull all the eggs and rinse any that appear to have egg splattered on them. Do not rub/wash them- only rinse to avoid removing the protective bloom. Then rinse your container and restart packing.
If you are uncomfortable using these eggs for some reason, then take a couple of the worst splattered eggs and cook them- inspect them visually, by smell and taste to assure yourself that they are good. I really don't expect any problems.
My early experience (and comments from YouTube) indicate that this method commonly has about a 10% failure rate. This is mostly due to eggs that crack and let in lime water (yuck!). This last year, I'd say that I'm down to about a 5% fail rate simply due to (a) being more careful when putting eggs into the container and (b) minimizing jostling of the container.
One additional trick: You don't have to create and add all of the lime water at once. I create 1/2gal of lime water and add to the bucket. Then I start adding eggs. As the eggs start coming close to the surface, then I make another 1/2gal of lime water and add it. Repeat until the bucket is full. The benefit of this method is that you don't have to reach down so far into murky water and are less likely to drop/break an egg when placing it into the bucket.
Good luck.