It's not a dumb idea, but I suggest that you think about your goals. Do you want a quick and inexpensive fix? Do you want something that's going to pass the time test, i.e., more than five years? Faux beams could solve your problem, but they could also call attention to the problem if they look "faux," i.e., don't fit with your home's architecture or structural layout. You may need to consult with a professional designer for input, to help you make informed decisions about what to do. Good luck!

Are there any other reasons that taking down the ceiling would make some sense, like electrical work, lighting, HVAC?

Could some or all of the disparity be addressed by adding strapping & another layer of drywall?

I'm not convinced faux beams are significantly less expensive than rebuilding the ceiling, particularly in the scheme of what sounds like a pretty major remodel. How deep are the rafters in each area? What type of insulation do you currently have and what would you be installing? How big of an area are we talking about?

Some photos of the area in question would be helpful for everyone to give you better advice.

@jslazart the contractor says it's 2 inches difference. Not sure what the insulation is yet. @ci_lantro great idea -- the new section was to have some recessed lamps pointing down, if they do redo the ceiling we can ask them to include the same lighting throughout the entirety now that there is access. I will ask about another layer of drywall to see if that's a possibility. Thanks everyone!