Hi heaterguy,
I am trying to be diplomatic to V1BLL. I have to make the measurements you are talking about on a regular basis since I design heater controls and PIDs for a living. I cannot see how a scope will help you in the least. Unless you don't care if your measurements are off 10-20%. Which I gathered you did care about, as your original measurements are probably 'that' close.
You haven't described anything else about your control system or what kind of heater or what the heater is in, and why you need the measurement so we are all kinda shooting in the dark er... cold here.
But you have stated(up top)that the "relay was at 30%". If you know the percentage and lots of time you can know this, because you can set controllers to fixed power settings, then my third option above works very well! Using a scope will drive you nuts for this kind of measurement and I wouldn't stake a dime on the results.
Another problem, again because we have no details, is the control signal to power translation. Zero crossing SSRs can have unexpected differences. Looking at the control side of an SSR DOES NOT give an accurate picture of what is happening on the power side. There are so many variables here it would take me an hour to describe.. It boils down to: If you want to know the power, measure the power on the power side. If the power control is varying constantly and you want to know the average process power, then take a long baseline average(minutes)(watthour scheme).