You have 2 vulnerable spots,,the hole for the cooktop and the hole for the sink. If there aren't already seams at those two locations, that's where they're likely to crack apart when you go to move them. Looks like you have a cast iron sink. Those are very heavy even without a granite counter top attached to it.

Even if you hire a granite company to move them for you, (because they have the proper tools, equipment and men), they're not going to guarantee that the counters won't break apart during the move.

Perhaps a fabricator on this forum can provide some advice on the move.

It's better to have a controlled seam than an "OOPS" break you have to repair in some highly visible spot.
Look for the seams and cut through them before you remove the granite
Re-seam after you have it installed in the new place.

Stone is hard, but brittle, and it doesn't stand sagging-type stress very well at all. You can cut plywood the size of the pieces and sandwich the granite between it for moving. Slide one piece under it, lay the other piece over it and clamp.

Get LOTS of muscle and use some sort of dolly that can support the piece on EDGE. Don't try to carry it flat because the stress will crack it more easily.

You'd be much better off getting a granite fabricator to handle the move for you. They'll have the equipment and experience at doing it. On the other hand, they'll likely require you to sign a waver that they're not responsible for any damage.

You're going to damage either the cabinets, or the counters using a multi-tool. You're not going to be able to save both of them without knowing that you will need repair of one or the other.

For the granite, if you can get the seams apart and the caulk from underneath, the key to transporting it is not ever setting it flat. You need to carry it vertically, on it's back edge. That means having a lot of hefty friends, a trolley, an A frame on a low trailer, and plenty of clamps.

Really, it's heavy enough that it can HURT you quite badly. It's not something that I'd ever suggest someone DIY unless they have all of the equipment above and have some experience in the past.

I am a fabricator.

We remove and reinstall several kitchens per year due to water leaks. Even with very experienced installers we always tell the contractor that breakage is possible because you can crack a sink rail easily even when you do everything right. The cooktop rails are even thinner and are virtually guaranteed to crack so your only option is to saw thru them and epoxy the joint at the new location. this is why cooktop cutouts are finished after the countertop is set.

if your seam is epoxied even after heating and scoring it you have to "pop" it loose and at least a 1/3 of the time in my experience the stone fractures somewhere near the seam but not the seam itself.

I would almost guarantee an inexperienced person or persons will have cracked pieces. Not a disaster if you can live with epoxied cracks at the new location.

Thanks to all. I'm learning quite a few thing and am going forward with oldryder's advice that I can expect to repair some areas when reinstalled. I'll precut at the center of the cooktop cutout -- at least I'll have a lighter and shorter L to deal with.

For what I'm getting for so little expense (there are four more sections to the kitchen which are not pictured) granite repairs are acceptable.

Two of the sections are short two-cabinet runs with granite counters. I'm intending to put in additional screws and some hand clamps to stiffen the connection between the individual pairs of cabinets and to move each section as a unit without attempting to remove the counter. That should work, umm right?

Thanks lazygardens. -- A bit of controlled precutting beats haphazard breakage. Plywood sounds like a good plan for the shortened L. We'll take the sink out first.