A budget gravel bike with an aluminum frame seems like a good option. The wider tires will keep the ride nice, and most of them have rack mounts. Mine has 40 mm tires, which I run at between 35 and 45 psi. It's a much nicer ride, and doesn't feel like any more effort than my road bike at speeds below 18 mph.

The drop bar does not HAVE to be low; even when they're high-ish, they're still more aerodynamic at speed, due to not having your arms spread out so far. They also give you 3-4 hand positions.

My road bike was more like $2k, but I paid extra for the belt drive and internal gearhub. You can get a similar class of bike with chain & derailleur drivetrain for right around $1k US.
I went one size smaller on the front pulley and two sizes higher on the stem, and now it's about perfect.


Priority Apollo 11 on a recent ride around town.