I think you have to consider this type of issue on several levels.
How much time / milage / hassle is saved by taking the shortcut? You can't blame HGV drivers for wanting to take the shortest or fastest route to their destination, especially if it avoids congension / road works or whateverm dispite the fact that the route may be more "challenging". The main route from Swindon to Salisbury (also the shortest route to Poole) is an awful road, very narrow, poorly maintained and realistically not suited to HGV traffic. However the alternative is either unfeasable or non-existant.
How much of the problem is genuinely caused by the HGVs? I appreciate that you said that the road is so narrow in places that it is extremely difficult for two HGVs to pass, but how much of the road is that narrow? I would suggest that the presence of an HGV causes no greater risk than a tractor / cyclist / horse on the same stretch. If other motorists are getting frustrated / not concentrating properly then you can hardly blame this on the precence of an HGV on the road.
If the road were genuinely unsuitable for HGVs then it should be signed as such, I'm not denying that, so maybe some of the problem lies with the HA / LA. If its a major route then it should be wide enough and properly maintained. Your point about being too wide to fit into a lane is very valid but then I see plenty of drivers out there who aren't capable of keeping a 6' wide car in a lane....
Thinking on a different tack, if the local villagers are campaigning for lower speed limits then the presence of the odd HGV is surely a good thing as in effect it makes the whole road a 40 limit....
