Ian, what you are describing is called a solvent cement. For solvent welding polycarbonate (which is effectively what you are suggesting) methylene chloride is an efficient solvent though IIRC there are other chlorocarbons that will work. Dissolving some polycarbonate pieces in it would make a good cement. As you suggest there are commercial products for this, a bunch of solvent cements are marketed under the name Weld-on but you will have look further to find something more specific. It doesnt look optimal for something you just want to hold something in place temporarily as the bond is permanent. Also the solvents are farily severe so it should really be an outside only thing unless you have a fume-cuboard. For solvent welding with methylene chloride a hypodermic syringe is reccomended to use minimal amounts, some sanding may be required to remove the abrasion and chemically resistant protective film which may be found on some polycarbonate. Solvent joins do not reach full strength very quickly so for structural joins you would still need something to keep pieces in place (though that doesnt say much about its value as a temporary fixing)
Alistair I suggest you just stick with the measure twice, drill once rule or use some epoxy which will at least leave you able to take damaged pieces apart again without breaking more things.