My guitar has that style of plate on the side, and about 4 months ago the screws wore out of the holes and no longer grip the wood so I've had duct tape holding it on since then which leaves the internal connection dodgy at best.
I've heard of the matchstick method of fixing this, is that the best way or are there better alternatives short of rewiring the jack to a new position?
The matchstick thing is pretty much the solution for a thread issue. All you need to do is fill the hole with matchsticks with a little glue to fill it out, cut them to size and you're done.
Matchsticks are the simplest and best solution. You don't even need to glue them in because the sticks are held in by the screws.