Ok, I have another more serious look at this. Here is a possibility:
It is possible to remove the left hand side panel without removing the seat. Get a hex driver into the hole and lever it up a bit and the sadlle has enough give in it to allow the hex socket head to be slackened. The other two are easy to get at. It might take a bit of careful manoeuvring to get the panel extracted from under the lip of the seat while negotiating the grab handle. I have to admit, I only had the rear part of the seat on when I did this - but it could well be possible.
I've attached a few photos, and I have stuck a piece of white tape just in front of where the rear of the side panel attaches to the rear cowl. (Mine had a crack in it from a while back, and it finally broke off while doing this. It now matches the other side !)
With the seat in place, you can insert a long screwdriver - use a Philips or a rod with a rounded end. A screwdriver blade will dig into the plastic of the rear mudguard. Insert it through the gap and keep it horizontal so that it meets up with the mudguard. There's a moulding obstacle in the way, let the point go to the left side of it to follow the channel, or let it ride over the top of it - but keep the end of the driver firmly on the mudguard. At some point you will hear a sickening metallic sound as if something has broken off - that will be the petrol tank support rod dropping out of its clip. That's OK.
When it is in far enough, you will have hooked the cable. See photo. Now this should give you enough movement to lever the curve of the cable to the left - ie towards the front of the bike. It provides a bit of extra movement in the inner cable, which when combined with pressing the lever, might be enough to release the catch. If the cable stop (green bit where the cable enters the bracket) has dropped out, then this will also pull the inner cable to release the catch.
[edit]I forgot to say - if the green cable stop is still in its correct place, then the cable end is firmly anchored and will not in itself result in the inner cable being pulled - but by moving the shaft of the driver along its length, it changes the shape of the curve of the cable - which can cause the inner cable to withdraw slightly - releasing the catch. So doing this while pressing the release lever will help to provide a little extra movement at the catch. I have tried this and it does provide a little extra movement, and this may be enough. There's a place mid way along the cable run alongside the petrol tank support accessory rod where you can move the cable up and down a couple of inches. This by itself will release the catch without touching the lever. But you need the seat off in order to see that effect ![/edit]
I've tried this action without the seat in place so that I could see what was happening and repeated it with the seat in place, and it is quite straight forward. You can feel that the end of the driver has gone under the cable. In fact if you keep the end of the driver on the plastic of the mudguard, it can't do anything but go under the cable as point where the cable enters the catch bracket is raised away from the top of the mudguard.
The only issue might be in getting the side panel off without doing any damage. Don't forget that if yours is a 2008+ model that the black / grey shroud under the panel (that surrounds the preload adjuster) needs to be unclipped first. Pull out the left (front) and right (rear) side of the grey panel - the lugs are just a push fits into a rubber grommit, so gently levering the panel out releases them quite easily.
PS - The same technique may well be possible from the right hand side of the bike - It is a longer reach, but there is no grab handle in the way to make the removal of the side panel more awkward. I didn't try this as there is not much room on my garage to work on the right hand side !
[edit2]You can tell that I am still thinking about this ! - A variation worth trying - removing the other side panel, and trying to thread a length of strong chord through might give a little extra movement - especially if you could thread it back so that it forms a loop over the cable. It might give a little extra ability to move it around. The cable runs alongside the mudguard towards the rear and then performs a tight 180 degree curve to enter the release lever mechanism from the rear of the bike. The only thing holding it in place is a groove clip moulding in the mudguard, yanking it a bit will release it from the clip and provide more flex in the release cable to play with - I've not tried this, I am just thinking out loud now.[/edit2]
Hope this provides a reasonably sound straw to clutch at. Its the best I can do I'm afraid.