There is no such thing as a 'more powerful SDR'.
TEMPEST has nothing whatsoever to do with what they achieved, it is actually very easy to intercept SOME video over a distance but it requires that the monitor uses analog drive signals to a CRT. Those signals are generally up to about 100V in amplitude and carried on fairly long cables up to the CRT. They inevitably radiate some of the signal and as screening them would degrade the video bandwidth, it was rarely done.
This raises two points:
1. any equipment that radiated that much interference would fail to meet modern EC standards.
2. equipment that radiated that much, pre-dates EC standards and also uses CRT technology.
An SDR or any other 'video sniffer' device cannot reproduce an image from an LCD or plasma display. Signals to those devices are digital and comprise clock and data streams at low voltage (or differential or both) levels. It is just about impossible to separate them from their combined 'RF mush' and even if you could, there are multitudes of data bit configurations you would have to try in order to discover the one used by that particular display type.
Another point is that the video bandwidth you could resolve from a CRT was very poor. You would not be able to read text for example, only shapes or large graphics.
Brian.