I'm going to just jump right in and recommend the C5 ignition kit. My '82 would periodically drop down to 3, 2, or 1 cylinder because the Pulse Generator was wonky and would not only fail to trigger the ignition coils at the proper time (or at all, sometimes) it gradually cooked the coils (repeatedly).
If you know it's only firing on one cylinder, I'd put plugs in all four plug wires, make sure they're laying across metal to ground the plugs, and hit the starter motor to make sure all 4 are even sparking (do this at night, it's hard to see the spark during daylight, but read the below paragraph about timing belt alignment FIRST). Since you said this guy got in over his head after something as simple as pulling the valves, you might not want to take his word as gospel about the compression.
You can also get a feel for the compression just by putting the bike up on the center stand, putting it in 5th gear, and turning the back tire. You'll feel more resistance as each cylinder goes into the compression stroke (assuming the heads are back on and the spark plugs are tight). If you're only getting compression on one cylinder, you'll feel one hard pull and three easy ones.
As for the timing belt, that's unlikely. If one of the belts (there are two) slipped, you'd still have correct timing on two of them and bitten-off valve heads rattling around against the piston in the other one. You can verify this just by pulling the timing belt covers and checking that the marks on both timing gears are pointed the same direction. If the timing belts have been taken off, the cams themselves (not just the valve rockers) have been taken off, or the head has been taken off make VERY sure you get them aligned exactly with the mark on the flywheel when you put them back together. The GL1100 is an interference engine, meaning that the valves and pistons are close enough that they can hit each other if they're out of time. More than one tooth out of place on the timing belt and you'll bite a valve off. I strongly suggest slowly turning the engine over manually (by the crank bolt or back tire, with the spark plugs removed) to make sure nothing makes contact before trying to spin the engine by the starter motor. If you hear a "tik" and feel sudden resistance, you'll be glad you didn't hit the starter button.