We used cherry slab doors for the lowers to get that somewhat mid-century look (our house is a mid-century as well - 1959). We had those soffits too, but we got rid of them when we renovated our kitchen.

Here is screenshot of part of our kitchen with the cherry slab lowers.

That’s well done! I like the way the doors and drawers cover up the whole cabinet and there’s no space between.

If you plan to live here, it's worth considering replacing the cabinet boxes for functionality. These old school cabinets lack the roll-outs and deep drawers that make accessing your gear so much easier. You could also play around with the layout. If you want to move in without spending a fortune on the kitchen, replacing the cabinet faces (I love veneer faced ply) or painting is a good choice. You can switch out the hardware and get closer to the look you're going for. I think you can replace the hinges and perhaps modify the the cabinet frames (need a professional) to get the inset look from the reference pic.

Your current cabinets are very ’60’s—true MCM. I’m wanting a 60’s style kitchen but those old style cabinets are super custom now. I’m compromising with slab doors, but your old doors are exactly what I wish I could have. If I were you, I’d spruce up the boxes/drawers and refinish/re-use your current doors.

Your cabinets are oak. In higher-end true mid century design the preferred woods were walnut, teak, birch, and sometimes maple. Your strong oak grains are what don't quite look right.

You could reface and put new hardware on. BLUM actually DOES make a hidden euro-hinge now made to retrofit to doors with that 3/8" inset. So you could have your current doors cupped and get hidden hinges.

If you want to tone down the oak grain and keep the cabinets, you could reface the bottoms and leave them oak with new hardware. Then have the oak grain filled on top and go white or a MCM color.

Here is a MCM influenced kitchen with two-tone top and bottom(although this is walnut).

Also, putting a bit of darker SPRAYED stain on your oak would hide the contrast with the grains some.