I'd be the last person to tell you it can't be done. Everyone said a 560M would not work in my G73sw, but guess what.... It does and rocks!
It is going to take allot of modification of your laptop. The heatsink needs to be rebuild using the plate of the 460m/560m (they are the exact same size) and the heatpipes from your G51. Then drivers will be an issue, but it could very well work the way I got mine working.
I know this is extremely rough but will give you an idea of how this would fit in. There are still many unknowns at this point, like what is inside were we don't see.
Here are a few pics that I matched the size of the cards and layered them on your laptop.
First the G51 from the underside:

Now your current 360M layered on to it so we can get a better idea how it's in there. I matched the MXM plug sizes. Again this is rough, but gives the idea.

And now the 460m/560m layered on. On the surface it looks like it would fit inside. You also have to think what's on the motherboard where it covers and the 360m does not.

The heatsink would need to be desoldered and the plate of the 460m/560m soldered on to your heatpipe. I'd still be a bit worried if that would provide enough cooling though.
Cost is also a big factor here. I paid 150 for a Asus GTX 560M with a heatsink and I've sold a Asus GTX 460M with heatsink for 100. My upgrade only cost me 50 bucks which was well worth it. You'll have to do much more work then I did, so costs can go up.
Anyway the point of all this is, don't let people tell you it can't be done. Do your own research and make your own decisions if it can be done. I knew for a fact I was going to get the 560M into my laptop, regardless that everyone on the interwebs was saying it can't be done.
Asus G73M (Used to be G73SW-BST6 now renamed to M for the Muratus edition)
- Intel Core i7-2630QM
- 1080p (1920x1080) LCD (upgraded)
- Samsung pm830 256GB SSD
- Sansung 750GB 7200rmp 2nd HD
- Bluetooth ( added )
- Blu-ray/DVD ( upgraded )
- Windows 8 Pro 64bit
Mods: