That's a good question!
I'm going to tag in
@tripletfeb @Sally PB and
@WingItRanch to see what their thoughts may be.
How far are you having to transport?
I would worry that the eggs would dry from being out of the lime solution and I'm not sure how well they would hold up.
Perhaps you can take them out, place them in a paper towel lined shallow container in a single layer (like tupperware/gladware), giving good cushioning with paper towels in between, then wet the towels with your lime solution to keep them covered? You'd need several containers, but it would keep them from jostling in the glass jars.