Good questions.
The reason I mentioned peak current is because the connector contact surface area has limits due to current density. Only so many amperes of current per square inch is safe, as contact area decreases the allowable current also decreases. A 1/4" connection has a very small area, therefore a proportionally small current for a given current density. SpeakOn connections gave a larger contact area (with higher contact forces also), thus higher allowable current.
Other important factors include the problem that when the 1/4" plug comes out of the jack on the speaker end, the tip shorts to the sleeve (inside the jack's barrel) and has the potential to damage the amp due to short circuit.
The third issue is that on a bridged amplifier (such as this), the shell of the 1/4" plug is not at ground but may swing as much as ~80 volts peak, and even more attention getting, the voltage between tip and sleeve would be ~160 volts peak if you happened to grab the connector while playing (or somebody else is playing)
Best solution is to have your cabinets updated to SpeakOn as well, and be done with it.