19V will still give you a reasonable output power- 40W according to the manual. That's can be plenty for most things with the decent temperature regulation.
Yes, if you have continuity from the outer barrel to the ground screw and tip then your mod is successful.
The 27V you're seeing is high impedance - parasitic capacitive coupling across the internals of the PSU.
As I said before, if you earth the ground screw on the iron with a thin length of silicone lead then you can still have an ESD grounded tip with the Meanwell PSU.
It used to be the case that 2 pin PSUs suffered from (a safe level of) leakage and 3 pin had grounded outputs. Now it appears that some PSUs have 3 pin and
some leakage (not sure how much less) - not a particularly helpful situation.
With C26 bypassed then at least you won't suffer from internal noise pickup and instability (the reason for the OP of this thread) if you use the grounding screw. It's worth giving it a try - you only need a thin ground wire so it shouldn't really get in the way if wrap it around the DC lead.
EDIT: Thinking about a convenient grounding point, you could maybe consider a rewireable IEC connector, eg.
https://uk.rs-online.com/web/p/iec-connectors/0488208/. You would need to be
VERY careful that your ground lead could not come loose from the ground terminal and accidentally contact the live one, using careful sleeving and strain relief. Just an idea.