Three way switch circuit leaking voltage

The 40V you are measuring is a typical value for a "phantom voltage". It is caused by capacitive coupling between wires, through the insulation, and usually in long runs of parallel wires AFTER the switch.

These couplings are high impedance and usually when connecting any load, the voltage will read 0. However, LED units (bulb & regulator) are high impedance loads at voltages below their operating voltage (e.g. 40V), and so it is possible they consume a bit of power even when the source is a phantom voltage. Regulators are notoriously short lived if they don't have enough voltage to work properly. Ironically, the transistors can overheat.

You can confirm this effect as follows: replace one of the lights with an incandescent (or add an incandescent to the load), and the voltage with the switch OFF should drop to 0.

Also, what voltage do you measure at the socket, when you disconnect the 3-way switch? And the other 3-way switch?

Your other point about the 6 month longevity with all bulbs usually suggests they are running at 240V rather than 120V due to mis-wiring somewhere. So to be sure: you are measuring 120V at the socket, between live and neutral (not live and ground), right?

And another check: you don't have weird issues when switching a 240V appliance on that suddenly lights get brighter, or circuits that don't work start to work? (This means that one of your two phases is not working correctly)

Update based on your 20V measurement: Yes by adding a load the voltage would drop, and since it drops by half (which is a lot), the phantom voltage remains suspect number 1 for the "faint glow". If you screw in something of higher wattage (20W...40W) like an old inc. bulb, I would suspect it to drop to 0V.

Are your LED bulbs dimmable? I appreciate that with your simple on/off switching the bulbs don't have to be dimmable. But, dimmable ones deal better with under voltage, they deliberately switch entirely off below a certain threshold, and that might help you here.

Update based on the LEDs being dimmable: The last thing I can think of is to try a different bulb / unit. Without cutting new holes for recessed/regulated systems, you could try a replacement just by wiring it up without installing it just yet. Not all LED bulbs and drivers are made the same, and you could get lucky (electrically, I mean).

The next solution would be to add a dummy load to the circuit after the switch. This is silly if you are trying to save power, but inc. bulbs are impossible to find. This is why we want to check the voltage (n OFF position) with a regular bulb (if you have one), to make the load a bit higher than with just under-driven LED lights.

Can you measure the voltage between the neutral and the ground, or the neutral and a neutral elsewhere in the house (use an extension cord). Let's eliminate a poor neutral as a possible cause too, since you have mixed problems.

The phantom voltage seems to be coupled after the switch, and so far we have the following possible solutions:

1. Move the wiring after the switch: this is lots of work, likely involves drywall repair, so definitely a last resort
2. Replace the lighting: this is a bit of a draw of luck, but some LED bulb & box regulators or integrated LED bulbs may have a threshold shutoff below which the LED switches itself off, rather than leaving it on, "leaking" and leaving a glow.
3. Insert a relay in the circuit right at the socket.

The relay has 120V switching poles (say 5A) and a 120V coil, and must be placed inside an electrical box. It will be wired so that the switch side of the relay simply connects the relay's feed to the bulb. It works as follows: if the voltage is too low, the relay is off, and the LED is cut off from the low voltage. If the voltage is high enough, the relay is on, and the bulb is fed the hight voltage.

There is the possibility that the relay too will switch on as a result of the phantom voltage. Should this be the case, we can experiment with a resistor placed before the relay, so that the relay's feed voltage (but not the LED's) is lowered enough to not trigger on the phantom voltage. It requires a bit of experimentation. Should you like this option, I can sketch you a diagram.