cobdomview I own two 2nd-hand Swifts because I was so impressed by the first one. I did have some issues with chain drop initially, and I can't now remember the full story of what I did. If the rear deraileur tension and limits are set up, it is very difficult for the chain to fall off at the cassette. If you could see in slow motion, a wave propagates along the chain when you change down or hit a bump and when it reaches the chainring, it is sometimes large enough to allow the chain to fall off. On my latest 20" wheeled bike, I fitted a Sturmey Archer FCSS1 (made by Sunrace) and these come with high guards either side. They also look smart. I'd recommend them just because the action of putting a bike in the car can derail a chain, and side plates help prevent that, and also help keep your hands off the chain. You can replicate this style by buying some slightly oversize 5-bolt 130BCD bash rings and fitting them either side of the chainring. jur wrote a FAQ on folding bikes in which he discusses chain derailment.
The subject of the seat post slippage is a thorny one. Some people argue grease is a lubricant, and therefore makes slippage worse, but others argue it fills up microscopic gaps between the seat pin/post and the seat tube and therefore increases friction compared to just air. The gaps might not even be so microscopic: I would bet that the tube only makes contact in a few places, especially after squeezing the slot narrower by tightening the QR seat clamps. Engineers blue or maybe marker pen might reveal this of you covered the seat pin and observed where it wore off when the seat pin slips or is rotated. I read that Swifts were given an unusually precise reaming when they were made (usually +/- 0.1mm is an acceptable "fit") but this sort of only works well when the same tension is applied at the QR, and there is no wear in the system. The second Swift I bought was almost a write-off because the previous rider had allowed the seat pin to slip and there was visible ovalization of the seat tube internal wall, and gauling/fretting of the seat pin. The gauling or fretting is perhaps another tick in favour of lubricant being used.
You will not be able to shim really small thickness because the shim will have tin foil thickness and no strength. Better options are to try a knurling tool on the seat pin (do you need a lathe to use one of these?) to increase the diameter a tiny bit, or to go for a significantly smaller seat pin diameter and us a more substantial shim. The latter is how I rescued the 2nd Swift I bought. A £7 digital vernier caliper (Aldi have these occasionally) is useful to work out what you are starting with, and a spreadsheet with common shim thicknesses and seat pin diameters will tell you which combination will give you the tightest fit. There is still some trial and error in it because of manufacturing tolerances on seat pins. Do you have a friendly relationship with anyone in the engineering department? You might be able to get some advice on preventing slippage/damage from them?

Having only a single ring at the front, I've sometimes wondered whether the Swift could be made to work with one of those 11-40+T cassettes; these modifications are often a money pit from the domino cascade of changes once you start, but living in Sheffield, you might consider it worthwhile. The Crossrack is worth considering as it can be almost completely detached bar the stub for folding and putting in the car, and a standard pannier can be fitted to it.