The purpose of the interrupted quench is to stabilize temps throughout the blade's varying dimensions before hitting Mf (martensite) finish.
You want to get the steel's temp below about 900-1000 degress so it won't revert to pearlite, but you want, as well, to stay ABOVE 400, or the steel will miss a fair amount of martensite.
As long as the steel temp remains above about 400 degrees, it will also be quite soft allowing for straightening before re-entering the quench media and taking the steel temp on down and the steel can cool evenly.
In this thread - so far - you have tossed around a LOT of terminology without discussing steel types, and/or austenizing methods.
The higher alloy types, like 5160 and 52100, WILL benefit from the multiple quench so as to reduce retained austenite, which can be a problem with steels normally requiring long soak times.
If you have taken a hyper-eutechtoid steel (above 0.84%C) to ABOVE non-magnetic and then slow cooled, it may very well be annealed to the point where it is capable of being drilled and tapped and threaded, but that steel now needs a MUCH longer soak time at austenizing temp to get every thing back into solution.
That another good reason for having a heat treating oven in that you can do a sub-critical spherodizing anneal where all of the carbon is pooled into small spheres (hence the name "spherodizing" anneal) allowing for easy workability, but then the carbon is in such a position that it doesn't need a long soak to immediately go into making martensite.
I spherodize every single steel I forge, after post-forging thermal cycles and reducing heat quenches to first create martensite and to then reduce grain size.
Lin mentioned an important subject about reducing grain size "within reason" since the smaller the grain size the more you reduce hardenability.
As well, make sure you are saying what you mean when you mention "normalizing". Normalizing refers to taking the steel way above the austenizing temp for that steel and then cooling back to room temp.
"Thermal cycling" is best done in reducing heat steps, first to well above austenizing temp, then to just above non-mag and then right to non-mag, and only cooling back to a black heat (1000) between cycles.
Kevin Cashen's dissertations on all of this are really worth reading, as long as you define the words within and really get an idea what he is saying.
I'll bet I find myself re-reading them about every 3-4 months.