Without looking it up in the Epson manuals, I don't recall the specific transportation instructions for these two printer models. I recommend you refer to your printer manuals and follow those guidelines as far as locking the print heads and transporting the printers with carts in or out (I know it differs depending on the printer model).
If you expect the printers will not be used for a few weeks around the time of moving, then I do recommend flushing the ink and charging the printers with PiezoFlush for safe storage and to prevent drying/clogging of inks in the internal ink system.
You can follow our guidelines on flushing printers, here: http://www.inkjetmall.com/tech/content.php?140-Flushing-Epson-Pro-and-desktop-model-printers-for-safe-long-term-storage-or-when-switching-inks
Dry and hot climates are the worst for inkjet printers, and I expect you will have to be more proactive at maintaining your machines that people in other areas. They keys to keeping a printer in good working condition are:
1. Maintain humidity levels between 40-60% and temperature between 65-80
2. Regularly use printers at least once a week, and try to not let a printer sit unused longer than two weeks (as pigment settling and ink drying can occur over time).
3. Regularly agitate ink carts to maintain in-suspension pigment (all pigment inks settle over time when left sitting still- this is true even with Epson inks).
4. Regularly clean the printer's capping station, flushing box and wiper blade as per our written and video instructions.
5. Dampers, wiper blades, flushing boxes and capping stations should be replaced every 1-3 years. Depending on your comfort and skill level, you can replace all these parts yourself by following the repair manuals, available at www.2manuals.com
I hope this helps!
Please let me know if you have questions or there's anything else I can help you with.
Best regards and good luck with your move~ Dana