I’ve done a very nearly full strip (not had to touch a poppet valve yet) a few times now…
As long as you’re not in a rush, you can do all of the job with only three ‘bespoke’ tools. Tool 1 is a set of plastic vice jaws with an 8(?)mm hole drilled through the joint, you’ll need this to undo the bottom cap from the inner post. Tool 2 is a length of 20mm plastic conduit with a mark measured from one end to the length of drop your post has. Tool 3 is half a dozen tie wraps to pull out the IFP (note: when you strip down the post, before separating the inner post head, compress the air shaft – this moves the IFP to the top of the inner post and makes it a doddle to remove)
The post bleed kit that is mentioned can be substituted by careful rebuilding and allowing settling time before screwing the inner post back together.
KS assemble their posts immersed in oil to remove the need to bleed, but just completely filling the inner post, then inserting the IFP, refilling, then inserting the centre shaft part halfway before pushing the IFP down into position then settling the centre shaft.
Top off the centre shaft then add the piston to close off the centre shaft, pour out the accumulation of oil from the top of the IFP.
At this point you can either just stick it back together, or leave it for a while so any air rises to the top. (I’ve done a few with just sticking them together with no issue)
There are two repair kits available, the first at ~£10 has all the seals required if you are just having up/downy issues.
The second at ~£40 also includes barbs, bushes for rotational problems and a host of other parts which in fairness if you need, the post must have been used as a crampon…
I actually have a post to do at some point in the near future, so will try and video this process!