They are fantastic plots - an artform!
The 5F6A probably has a relatively 'stiff' screen voltage (given the choke and cap, and not huge screen stoppers). Maybe that is associated with not identifying a curved 'down' end for the good resistive load plot - as the plot indicates it has hit saturation voltage and then travelled up a bit in current as grid is pushed into 'conduction' zone (the 5881 datasheet curves certainly show that character). If the screen was sagging under load, then perhaps the anode current would perhaps hook the other way a bit. If you get inclined, maybe repeating the resistive curve at a lower frequency may show up some screen sag.
The 'intensity' of the screen persistance indicates the time spent in that area - so the time spent at seeming high peak power dissipation levels is effectively average down - that power chord plot on the LHS is reminscent of switching losses in a switchmode. The 'wacky' one would have some high plate dissipation - what did you 'play' for that one?
Do you think the negative voltage excursion in the 'wacky' plot is clipped by the screen edge, or just not easy to see? The positive voltage peaks seems to get to about 1-1.1kV (ie. maybe up to 800V from B+), and it sort of looks like it goes negative from B+ by about the same amount - which would seem appropriate.