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Hello Perry and welcome to the forum.
From your description it appears that you did the measurement correctly. There is always a chance of instrumentation error when working with RF but a factor of five error would be unlikely with a scope.
Regarding the higher voltage peaks during modulation, this is to be expected. At 100% modulation on an AM signal one third of the total power (one half the unmodulated carrier power) is contained in the sidebands and this power adds to the unmodulated carrier power. Remember that using 0.707 x Vpeak only works with a sine wave.