You can "kill two birds with one stone" by doing a multi-piece back. Sides will generally be less "swirly" (as Michael N say) and easier to work so get an extra set and use some of that with a back set or even instead of one. Put in ebony strips between the pieces and a 3, 4 or 5 piece back will look really nice. Romanillos did at least one cypress guitar with a strip of satinwood right down the back. I put a picture in this thread: viewtopic.php?f=42&t=105106#p1118353
The courtnall book also shows a Cypress (Santos Hernandez) with a multi-piece back. Somehow Cypress and ebony just seem to go together.
Romanillos suggests 2.5 mm for Cypress backs but I didn't see any specific side thickness mentioned. I would be thinking of about 1.8 mm but to be honest I don't measure it very precisely - I do it by feel but "bendy enough" it generally turns out to be around 1.8.
Beware that Cypress sometimes has areas that "break out" so be diligent about picking a "good side" (both for back and sides) and protecting it once it is nice and smooth. The waist can burn easily enough when bending. Thin sides bend easier so another reason to go thinner. I am not brave enough to go down to 1.2 or whatever Torres is reputed to have done on some guitars.
I think pretty much any decent classical plan will work well: Torres, Santos Hermandez, Ramirez 1912, Romanillos and no doubt lots of others. If you already have a nice plan you are familiar with just use that again. Understanding the plan you use is probably more important that the specific plan.
For sources I have also used Madinter and Barber and also Espen in Germany. Due to funny German customs issues I have not bought from Turkey. As this is an "urgent" project I would suggest asking if the supplier has some older stock. Or even approach a luthier who might have some older sets available. By older I mean something that has be stored for 5-10 years as opposed to a year or two since harvest. I would stick with the so called Mediterranean cypress as it is the tried and tested traditional option. Beware that the smell when working it is very pungent. "Stealth mode" work would be impossible.
Good luck with your house move too. I hope the new place is to your liking.