Not sure if this is what you mean. This a house we are buying so I can’t give better photos.

It would look horrible. You'd have to add a soffit, which is a dated look outside of certain mid-century designs.

No false front. Your vaulted ceiling is something you have to accept. However, your current upper cabinets have a crown color that is different from the cabinets (oh, the '90s!). It will look better when your new cabinets' crown matches the cabinets. You may want to get white cabinets so that the contrast with the vaulted ceiling will not be as jarring. The current wall color is also adding to more contrast with the ceiling making the slope of it more jarring.

In your renovation, I'd see if you could put canned lights into the slanted ceiling (you can adjust their tilt to point down). Having lighting up at the ceiling, rather than the track lights and small low pendants you currently have, will also help to minimize the sloped effect.

I don't think a soffit that is exactly the depth of the upper cabinets and is the same color as the ceiling or the same color as the painted cabinets, so it does not call attention to itself would be the worst thing in the world.

I don't see how to fit a soffit under that ceiling without using upper cabinets that are only 30" tall, i.e. shorter than she has now, which hinders their storage capacity and creates a horizontal squat look. Not an improvement over what she has now.

The gap is fine. We had a vaulted ceiling in our previous house. We lined up the back of the cabinet with the top of the wall so you just have a small gap at the front. We installed LED strip lighting above so that at night you didn't get a shadow line from the recessed light. We only used that if we had guests over at night.

Don't have a great photo ... I was photoshop-ing in pendants during construction, but you can see the gap at front.

This is a non-issue. Of course the wall to the left had an even bigger gap, because the ceiling sloped up over those cabinets. I wouldn't have given up the vaulted ceilings to have a generic look for the cabinets!

The cabinets could be exactly the same height as they are now, or higher. They could be hung all the way to the junction between the wall and ceiling. I am not talking about some gigantic looming thing that is tall and deeper than the cabinets. I am talking about something that feels in that angled gap, nothing more.

This is a lousy soffit. It is necessary because it has ducting inside. It's deeper than the cabinets, it hangs down more than the height of the duct, it sticks out in front of the window, it's badly built. This is what most people think soffits are because most of them are built like cr@p.

This is also a soffit. It is also necessary because it has ducting inside. However someone paid attention when they were building this one. It is slightly shallower than the cabinets, it is perfectly level, it does not overlap the window. It is no taller than absolutely necessary for the duct.

You can get custom cabinets that are angled at the back and actually fill that space. You wouldn't gain much, though. A soffit like Palimpsest posted (the good one) will actually look good. You can still have crown molding with some thoughtful planning.