Oven flame modulation

This is a Hardwick gas 20" apartment range with pilots. Operates on natural gas. I suspect this stove is from the 1950’s. The oven heats to temperature but gas flame shuts off completely when it reaches temp rather than modulating down. When heat is called for it ignites "full on again" then shuts completely down again at temperature.

We recently moved. Stove worked OK in former location. Upon lighting the burner pilot in new house I noticed the pilot flame was over 1 inch high. Adjusted pilot down to normal level. Oven pilot is OK and extends to sensing rod when oven is turned on.

I’m suspecting higher pressure gas in this new location. Did not use a pressure regulator in former house but I have used one in the past on another old gas range. Could my oven control problem be due to higher gas pressure at new location? If so, what "in line" regulator should I purchase?