The stereo jacks thing is something I have recommended for other reasons before. The idea of it suiting more amp switching systems is a great heads up. In a speaker socket it allows you to reduce the contact resistance by soldering the Ring and Sleeve together as they both contact the barrel of a mono plug. You MUST be careful to insert the plug before firing up your amp as inserting it with this wiring will actually briefly short out the Tip and Ring on the way in. Some amps may not like that. It's fine if it is already inserted fully when you switch on.
In your guitar it also helps to replace the usual mono TS open frame version socket with a stereo TRS version and also wire the Ring and Sleeve together. It gives you two contact points for the ground which helps noise much more than crappy thin copper foil. The usual "slip in sleeve" ground connection for that type of socket can cause intermittent problems when it ages as there is actually no sideways force pushing the plug barrel against the socket sleeve. You can even sometimes feel them rattle slightly in the socket. With an additional sprung ring contact there is a sideways force from the offset Tip and Ring blades which achieves this and gives that better ground security.
I'm not sure if you picked up on this from the original posts here bu just in case, if you are using your footswitch with the H&K setup you need an LED inside it in series with the switch without any resistor. If you wire the LED across the switch you will make the amp think the switch is permanently closed as, when the switch is open, the LED then acts as almost a short to the line in place of the switch. In series it will work in the same way as the LEDs inside the amp. So you should wire it as: Plug/Cable Tip in -> LED anode; LED Cathode -> Switch Contact 1; Switch Contact 2 -> Plug/Cable Sleeve. Switch Contact 1 and 2 should be the centre wiper terminal and either outside one.
I'm not surprised you will get a response from your LED when you meter it for resistance. The meter puts a voltage across the probes and measures the current that it takes. If your LED happens to be across that you could well light it up slightly. It's usually at a high enough impedance that it can't cause any real damage to normal circuitry.
In my day job, (retired now), I used to design electronic circuitry for the audio and then the seismic industry and I also programmed for the seismic and defence industries too. Now I just make a nuisance of myself poohpoohing the lies, myths and legends of the music electronics business. And there are MANY! And it's a great pool of people wanting to desperately believe those lies, myths and legends. Sadly, you can only make a few of those people think about it before believing. All good fun.