Are you sure the LED is blown? Shorting across the reflector isn’t too likely to damage the LED in this light since the input voltage is a single cell and the driver is direct drive. i.e the driver is basically already shorting the battery across the emitter.
If the minus solder blob contacts the emitter, you end up with a single mode light stuck on high. Possibly you’ll also notice a small increase in brightness because you are now grounding the led through the body of the light and bypassing the tiny LED- cable that runs to the driver. I also had one light that gave me Phantom strobe and sos modes in this situation, just a very faint dimming by the driver rather than full on and off.
If the plus or both blobs contact the reflector the driver will short across the reflector, the led won’t come on and you will either immediately trip the short circuit protection on your protected 18650 or you will have a very hot and bothered battery and possibly an explosion on/in your hand. If that’s what is happening in your light, don’t put any unprotected cells in there, could be quite dangerous!
I’m not sure about this but it may also burn out some driver components if the current is high enough for long enough, maybe this is what happened in your light and the led is fine but the driver is toast?
Best way to check the led is to get a fairly well drained 18650/26650 cell <3.6v and hook it up directly to led wires. If there’s no light or it only glows faintly then you know it’s dead for sure! 
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In any case I can’t argue with wanting to change the stock Led, whether it still works or not! Rip that blue fella outta there and replace it with something decent
I’m not sure if you’re aware of this but the straight driver swap is a little complicated on the HD2010. The stock retaining ring that holds the East092 in place isn’t directly compatible with any of the 8x Nanjg 105k based drivers like the Qlite or KD 7135v2 drivers. Basically it doesn’t work with any driver that has components on both sides of the board. And the pill being aluminium means you can’t solder the ground connection for the new driver directly to it.
So you have two options.
You can get some of these Brass ring adapters and solder the above drivers to them then press fit the whole thing into the stock pill and discard the retaining ring.
Or you can get a Nanjg 101-AK-A1 4x7135, that only has components on one side, and stack the living heck out of the 7135s on the back!
Like this
But this is really fiddly even if you’re comfortable stacking an extra layer of 7135 chips. The benefit is that it’s really very neat once assembled and with this amount of 7135s the light is theoretically regulated at a maximum of 6Amps but in all practical applications it’s direct drive just like the East092 it replaced.
Either way you’ll need to get a total of around 12-16 chips on there to get close to the output that a good HD2010 with the east092 can do on high. At the stock 3Amps you’ll get from a Qlite it’s going to be a bit of a step down in total brightness, provided your HD2010 was operating as it should have been.
Other than these caveats the Qlite is a very nice driver with a great selection of modes so it’s a very good starting point.
Oh man that was some serious rambling, hope at least some of it was helpful.
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To sum up.
If you’re looking for off the shelf components, maximum output and a simple mod. Keep the East092 and replace the LED.
If you’re up for a bit more of a challenge and/or really hate blinky modes then the Qlite mounted in the brass sleeve with some extra 7135s stacked is the way to go.
If you’re sadistic and anal about keeping the stock retaining ring, then the Nanjg 101ak with custom firmware and a triple stack on the back is the perfect solution 
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Best of luck with the mod!
Linus
PS: A final and more expensive approach would be to buy a copper pill offered by Ryan in this forum, then you can solder the drivers directly into the pill.