Having found a replacement for the lost original old-style spool, I picked the ASSA Twin 6000 again, this time in its original configuration. It was far more difficult to pick with these deeper spools installed. The reason for this is that the lock would fall into a far deeper false set when picked to the countermilling and no amount of upward pressure on the pins would give any feedback or lift them out of the position. The images below make it clear why this is. The countermilling is deliberately matched to the spools causing them to lock in place and bind up.
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The solution was a three-phase system:
Phase 1:
Pick to a false set, making sure not to lift any of the driver pins up past their countermilling and up to the sheer line. I know this is counterintuitive, but later you will need to know exactly where you are in your progress on the top pins. This particular lock only has countermilling in five of the six chambers. A little trial and error should allow you to identify this situation if it exists. If picking past one click oversets the pin, you are working a chamber without countermilling.
Phase2:
Pick the sidebar, looking for a distinctive deeper false set that indicates you are in the true gates. Often there is a cool sounding sharp "thunk" associated with this. This sound makes me happy
You can sort of confirm that they are set by tapping on them and seeing if they are tightly bound or a bit loose. You want them to be a little loose. At least in this lock, I would not bottom out the spools until after the sidebar was fully sitting in its true gates.
Phase3:
Return to the drivers, using the counter rotational force provided by the sidebar springs to apply negative tension on the plug. Rotating it back will allow the careful lifting of the drivers out of their countermilling.
When picked this way in phase 3, the drivers behave much like standard spools, except you are replacing the counter rotational force that would normally come from the upward pressure on the pin with the spring tension from the sidebar. This means that you are picking them basically blind which is why it is so important to not to inadvertently lift any of the drivers past the countermilling to the sheer line during the first phase. Doing so would cause you to overset the pin during the third phase. It is VERY VERY easy to drop side pins during phase 3. It is infuriating when this happens but the situation can sometimes be salvaged. Often though, you just have to reset all five side pins and start phase 2 over again. Regardless, keep very close track of which tops pins you have lifted to sheer. Again, you don't want to overset them when you return to phase 3.
Reading some of the writing that XEO has done, it is clear that there is a high degree of variability in these locks. Both with how difficult / possible they are to pick, as well as the interaction and timing of sidebar engagement. I don't imagine this technique will work with all, or even most ASSA Twins that have the older style drivers... It's just what worked for this particular lock, and might be worth a try if you are finding yourself in a similar situation.
There were many times during my work with this lock that I thought it was simply unpickable. It's just a lesson to me how important it is to always think creatively when I find myself against a metaphorical brick wall.
I hope this was helpful to someone. FWIW, here is the video of me picking it:
https://www.youtube.com/watch?v=GlrKKtuS1dQ