Jump start. Measure voltage with engine running -- 14.5V
About right, but...may be the battery not holding the voltage output back.
>Install new battery (old one 7+ years old). Drive about 10 miles.
>Measure voltage with engine running -- 13.95V.
About right again, with engine running a few minutes
>Turn off engine. Voltage at battery -- 13V. Too high, right?
About right. The extra volt is surface voltage and soon drains off. You need the extra voltage pressure to push the charge into the battery
>Start engine. Voltage -- 16.7V!! Wow. Not good.
Could be correct, if you just measured the voltage at startup. Run the engine for a minute to see if the rate goes down. It may be the high initial output is a result of the drain from the starter
>This means bad voltage regulator, correct?
Solid state regultors usually work or not. There is an amazing difference in the output between regulators, meaning 10 new ones in a row may not put out a consistant rate, but have a range of rates that are acceptable.