Sounds from what you are saying that you reckon you can just about get the blades out without touching the washer. And I see there are several more pictures in your album. Judging by the chamfered blades, this is one of the smaller sized collets, like around 1/8" (ie biggest blades) so possibly the most tricky to dismantle. Can't read the size from the photos.
There seem to be variants on the design, such as the ones shown in this thread. The interesting things is that here the washer is held in by screws or bolts, which rather supports the suspicion that the washer is what holds the blades in place.
As your slots and blades are bunged up at the moment, it won't be easy to compress the body much at all. However, after cleaning up it may be possible to compress the body enough to remove the washer. How deep is the groove and what clearance do you measure between the blade and slot, once cleaned up? You probably need a special tool to compress the body with these non-bolted examples, which may the main reason it's proving so challenging.
To clean the blades, I'd use a green pot scrubber fitted to a power sander (the sort with the hook and loop pad) and loads of WD40 / Gunk etc – and some form of blade to get the scrubber into the slots in the body.
Murray