Is there any reason you can't put flat handlebars on a road bike or
drop handlebars on a mountain bike?

Yeah, if you try to retrofit either way you have issues with bar
diameter, stems, shifters, derailleurs, and so forth. It can be done
but it may prove more trouble than it's worth.

My advice (FWIW) would be to go with an inexpensive 'cross bike with
flat bars, 622 rims and 32 tires, flat bars and thumbshifters with
cheap Shimano 7 x 3 gear on it. No suspension.

OK, you can have 9 speed if you insist.

This is a pretty good package for the riding you'll be doing.

I don't know how many times I've seen people say "I will be riding
on dirt X% of the time," but trust me, you'll mostly be riding
on pavement (note to British readers, we think of "pavement" as
the road rather than the sidewalk, as you do).

A couple of bar extensions (bar ends) will make this better, but
just the short ones are fine. Another hand position.

You might as well get a steel frame, they are slim and pretty as
opposed to aluminium which is fat and ugly.

Cantilever brakes mean you can get fatter tires and fenders.

Get a rack, the best are not as much more expensive in the long
run as the worst. If you choose carefully you will do well.

What I think you want is a bike that is appropriate, you might
consider this as in the nature of a suggestion.

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