Hi WardL,
Yes you can get your tyres rebalanced. Balancing is part of routine servicing but is normally done on a need basis. The weight of a bit of rubber can be counteracted by a lead weight. Unless they are badly gouged 10 or 15 grams of lead may do the job.
Shaving tyres is an option I haven't heard of before, except with retreads where they basically lathe (think crude lathe type machine) the old tread right off to leave a coarse surface to bond the new tread on. Thankfully retreads are not used mch any more. A hole in a case of a retreaded tyre will often cause a bubble between the casing and new tread which will lift the tread and cause the inevitable tread shedding.
If a tyre is regrooved to deepen the tread available this will change the balance and also require rebalancing.
Other option is to go and have some fun converting them to smoke. BUT, as we know, real men smoke Bridgestones.