It's not all that bad in Missouri.
Straight off the Mo DMV site:
"A vehicle that is registered as a historic vehicle may be driven:
- To and from exhibitions and educational events without any mileage limitation;
- To repair facilities within a 100 mile limit; and
- Up to 1,000 miles per year for personal use.
The owner is responsible for keeping a log of the miles driven for personal use each calendar year. The log must be kept in the vehicle when the vehicle is being driven on any state road.
Historic vehicle registration is a permanent registration and cannot be transferred. If you sell or dispose of the vehicle, you must remove the plates from the vehicle at that time."
The only mileage you have to log is personal use miles. (here)
We drive ours everywhere all the time. As far as getting stopped, as long as you're obeying the law, there are no worries. (here)