The article on the T-ABC special files site, by Terrance J. Van Parys is an excellent start.
I followed most of what Terrance wrote, but I may add some additional text for those who wish to fully dismantle the dampers.
The circlips you refer to are shown in one of the rare cross-section figures of a damper and it is in the Brown book. You will note that the circlip is shown located between the two pistons. There are lots of tiny arrows that help the reader understand the fluid mechanics of the damper when operated.
The circlips orientation, and that of the pistons themselves are important and can be determined from the Brown book.
Regarding the core plug - I removed this by drilling several 5mm diameter holes through the plug in a horizontal line, such that with 4 holes, the diameter of the plug was compromised in strength and can be levered out. Under the plug is a red/maroon coloured seal (as per Terrance's article).
There is nothing else holding the shaft in place. The shaft is an interference fit only, between the splines of the lever shaft and the actuator arm that moves the pair of pistons internally.
I did not use a machine shop to press the shaft out. Rather, I used a 6 inch vice and an arrangement of two old shackle bolts (with nuts attached) positioned one over each damper mounting hole and a small socket to fit over the shaft end (as revealed under the core plug. By application of the vice, this provides thrust directly along the lever shaft.
I was concerned about the bending moment when tightening the vice, so applied additional lifting force by driving wedges in the ~4mm gap between the lever arm and the damper body. Two such wedges, plus the pressure from the vice (all coordinated - need 3 hands!) was sufficient to safely drive the shaft out.
Once free, the actuating arm inside the damper and between the pistons can be extracted. Then with the end caps also unscrewed, the piston assembly can be withdrawn complete.
Please note the orientation of the piston assembly - there is a 'way-upness' to them. Also note, that the circlip has a way-upness as well (see Brown book).
There are 4 circlips - in two pairs, arranged with one pair on either side of the piston pair, joining them in the center and either side of the actuating arm.
Further, there is a thin rectangular plate that is trapped underneith each pair of circlips on either side of the actuating arm to provide a separation limit between the pistons. The circlips provide a thrust pulling the piston towards the actuating arm.
Once the pistons are removed, each has a valve at its end. There is a flat sprung steel plate that can be prised free, under which is located a round brass plug of about 5mm in diameter. Remove the plug and a circular thin sprung steel valve can be removed from a circular backing plate with holes. This plate can also be removed, to reveal a brass gause mesh/filter.
The rest is straight forward. On reassembly, be careful to check that the lever arm splines find the correct position relative to the piston actuating arm splines, as this orientation defines the arms neutral position. It is worth noting the full extent position on a second damper and use this to define the limits of the repaired damper before you repress the level arm shaft fully back into position. The travel limits of the level arm should not be less that the vertical travel limits of the axle between top and bottom bump stops, and should be the same on both sides of the car.
AND AN ADDITION:
One other little tip - when the lever arm has been removed from the damper body, it is a good time to replace the rubber bushings. It seems far easier to install them when there is just an arm.
I do not have the bush fitting adaptor kit, but found I could insert the rubber bushings first, then drive the shock link stud or arm using a vice and a pair of screw drivers, lubricated with some saliva and copious invective.
Also, if part of the purpose of your damper work is to repair the leaking seal around the lever arm, then Terrance's article identifies the correct seals. I bought 8 last June, and a further 8 later last year. They may have some in stock, but it seems from my discussions with the lady (name of Ina, GDFriend@allsealsinc.com) at 'All Seals' in LA, that we MG-ers are the only customers for this partucular item!
Sorry this has been a long discorse. Hope it helps.