It may be better to just dig up a few of the plants and their roots and place them in pots to take with you.

Unfortunately the rosemary plant is HUGE. So that wouldn't be possible. But maybe this would work for the mint.

For the rosemary I'd try to take cuttings now and get them rooted in pots before the move. Rosemary, for me, roots better in potting soil - just cut, remove lower leaves, and stick it in moist potting soil. If you have rooting hormone or some honey handy, you can stick the end of the sprig in that before putting it in the soil to help encourage root growth and inhibit fungus. I'd probably do a few because some may fail to root.

Mint you can just dig/pot some up, or stick several sprigs water - mint roots very easily in water.

While rooting, keep the cuttings in subdued light, like in the house near a window, or on a shaded patio until obvious new grown begins. Then they should be ready to be planted out - although if you're getting there July-ish(?) it may be a bit hot. If daytime temps there are consistently over 90-95+F, you might consider keeping your travellers in pots until fall when they'll have a better chance of taking root in the new garden.

abq bob,
thank you so much! I'll start several cuttings of both today.