Hey... I'm back from overseas... yay!
OK, you say the turn signal on the dash stopped working... do you mean that it DID work at first (after the modifications) then stopped later, or it never worked after the mods? I'm going to assume it never worked.
As an "LED bulb" it will already have a resistor built into it so it doesn't blow up on 12V. This means that it should read the 8.5V as close enough to 0V and the 11V as close enopugh to 12V, therefore there's enough difference for it to flash. My bet is that what you're missing is a good earth. The way the dash turn signal light is set up is to earth itself through the opposite turn signals... ie: if you turn on the left signals the left wire goes high & low and the right wire provides an earth through the lights on the right side of the bike. A standard bulb has a resistance close enough to zero to act as a normal wire, but as I mentioned earlier an "LED blub" will also have a resistor built into it. When you put an LED & resistor combination (the bike's turn signals)on the earth side of the dash light that can be enough to stop the dash light firing.
Further, LED's only work in one direction - they're just a special sort of diode which is like a valve for electricity. Unless your bulb has been specifically made to work in both directions you'll never get it to do what you want.
Try this:
Take the "LED bulb" out of the dash turn signal
Attach one end of a wire to the "left" wire in the socket, and the other end to one of the bulb's terminals.
With a second wire, attach the other of the bulb's terminals directly to the negative terminal of your battery.
Now turn on the ignition and switch on "left"... I bet the light flashes?
If so you've found your problem... insufficient earth, due to the built in resistors in your turn signal "bulbs". You'll need to modify the wiring to the dash light to add a third wire for a decent earth (there's an earth supplied to the tacho/clock socket), use a couple of regular diodes to connect the left & right wires together without them feeding back to each other, connect both the left & right sides to one terminal and your earth wire to the other terminal. It's a fix for a stupid problem that has been plaguing British vehicles since the 1960's or earlier, that Triumph used to save a few bucks.
There's details on my website in the "LED Console Lights" page.