Can I re-shim the strike side of my door jamb to make a 28" door fit?
Depends on how big of a gap that you have that is currently being shimmed but yes this would be the easiest thing to do.  I would make sure that you have at least 3/16" gap at all points before doing this.

Note:  Just to be clear you should be using the new jams in this door.  At the very least you need to use the hinge side but preferably both.  After you take out old jams (top can stay if it is going to cause a ton of work - and most of the time it doesn't) you install put the new ones in.