Thanks for the informative replies.
I modified the circuit (bottom attachment) and now have the gate voltage under control and have switched to the IFRZ44N with no issues other than it appears to be clipping the the peak voltage which I assume is when it is in avalanche mode. As it stands I could sail forward but would like to tame the overall current consumption. Another issue is that when I put a 100 mega ohm resistor across the zapper electrodes this seriously dampens the zappers output. All circuits that I have seen like this have some sort of bleed resistor across the electrodes and I thought 100 M would be adequate.
The mosfets are all either purchased from Mouser in the case of the IRFZ44N or salvaged from various other legitimate donor boards in the case of the IRFZ46N.
I think the transformer winding ratio is way more that a 1:1 ratio but have not tested it. For some reason I can't use my signal generator to calculate it. Maybe I need to take the transformer out of circuit. I do know that the primary is 38 turns or thereabouts and the resistance is on the new falstad sim picture below.
The unloaded output comment has me curious because I don't know what to call the load. Is it the Bee when it gets zapped? I did hook the bleed resistor up across the electrodes and all it does to the wave form is increase the frequency with the same voltage peaks.
Is there a proper way to put a snubber circuit on the output to keep the peak voltage within the limits of the mosfet?
I have attached some new pictures of the output wave forms, and the little board arrangement that I cut out of the laser printer. It is a meaningful project in that these Bees which are actually meat wasps have terrorized our property during the past three summers. So much that you can't even sit out on the porch and have a beer without being attacked.
The goal is to modify some small grates so that I can just put the grate over a tupperware tub (most likely yellow) full of a bait like salmon or some other fish and see if they will be kind enough to complete the circuit I'm working on.