I would raise the DW to the height of the counter. You could add 1/2 inch tile (or shims) for each corner of the DW legs. But, then you'll need to add base molding to match the base cabinet molding to fill the void in the bottom of the DW.

I always include an extra filler when planning my kitchens. The filler is used to bridge a gap that may occur like in your case. It also gives something for the DW to mount to if it has top mounting tabs.
Any chance you have extra finished material from the kitchen? A cut off from a panel, etc?

Design Lift... we don't have extra anything yet. The contractor and cabinetmaker coming by today. We remodel is not done, we are in the middle of it, so I think at this point, they can work out something and make whatever we need to make it look good. They will even lower the cabinets, but then they'd have to float floor above cabs, in effect making them lower. That seems like a lot of work to me. But they and my husband and I have the meeting today to discuss our options, before everything is set in stone (literally), and adjustments can be preplanned.

Design Lift, one more thing.... do you mean a filler to go on the bottom or top? I'm leaning toward getting a granite grabber thing to attach to the top, because a wood piece, as my contractor suggests is standard, would make the bottom be below the counter. I know it would blend, but I really want the DW as close to counter as possible.

The filler I mean would go between the top of DW & underside of counter. If your DW legs won't carry the height, it's a common thing to do. Especially if your DW only mounts (secures so as not to tip) from the top. If it mounts from the side, the filler wouldn't be needed except to fill a possible gap.

Design Loft, our DW has two mounting options.. one from the top, and another from the inside of the tub, which is super weird and my husband won't do it. So I'm thinking we will raise the legs, and maybe put something on the bottom to bring it up a bit. Or float the floor higher just in the DW area (there will be ceramic tile). That means we will need a new front thing at the bottom to be fabricated, if the supplied one looks funky.

I made my kitchen counters taller than standard and just added a lenth of plywood of the right thickness, front to back where the legs sit. The plywood is about 6 inches wide. The toe kick adjusts and covers it all.

I have done exactly per Jakvis' solution. 5 minutes of time and some scrap plywood. Dishwashers have been made to attach at the sides due to difficulty of attaching to granite and the like.

IMHO, both options are just fine. In fact, over the years, in different kitchens I have seen both and unless you know what to look for you'd never notice.

You can raise the bottom of the dishwasher. The downside is that the toekick won't align with adjacent cabinets. Sometimes, you can hide that difference by installing a panel to the front of the dishwasher that extends a little bit lower. But often that's impossible and will prevent the dishwasher door from opening fully, as the panel now hits the recessed toekick.

You can also install a filler strip at the top of the dishwasher. It's just part of the cabinet and won't stand out at all.

In our case, we raised the countertops by a full 2". A filler strip would have been fine, but instead we opted to install a pull-out cutting board. It looks very intentional and nobody would think it is out of place when they just look at the kitchen. But I have caught myself once or twice pulling out the cutting board instead of opening the dishwasher. I am sure I'll get used to that though. That's just an issue of getting used to a new kitchen.