Top tip for anyone with an A-TEC Maxim or any other modular type of moderator who finds they can't separate the individual elements for cleaning just using their hands to grip it.
Find an offcut of 1" thick plywood and cut two pieces about 6"x3". Get a suitable sized hole saw and put a hole (1 3/4" for my Maxim, 1 1/2" for the CMM) at one end on both and then make a 'V' shaped cut from the other end up to the hole.
This will allow you to get extra purchase on the moderator and use a bit of leverage to assist in undoing it.
If this doesn't work then next stage is to clamp one piece in a vice and then use an 8" or 10" G clamp on the other piece - you don't need a lot of compression force, just enough to stop the wood turning, but the extra leverage the clamp gives will get most seized moderators apart.
I also have a pair of these for A-TEC CMM moderators as they are steel and are prone to rust especially if used in humid or wet conditions... even when given a blast of WD40 after being used.