The simplest solution here is to dig out a few inches around your existing concrete post footings and add additional concrete mix to the dug out area. If you do this now that the ground is dry you should be good-to-go for the longer term.
Note that even though the post holes were originally 28" to 32" deep you would not really need to dig down that full depth when you enlarge the holes to make things more sturdy. If you were to enlarge each hole 5"-6" all around to a depth of 10" to 12" and full that entire enlarged area with concrete the fence will be a lot sturdier.
The reason this would work is that the greatest area of motion on the posts as they wobble is at the surface of the ground and not at the very bottom of the original holes.
Depending upon your geographic location you may have to consider frost depth onto the ground in winter. It may be that your original hole depth is not even adequate for your climate zone. In addition the proposed shallow fix may be detrimental to your fence if the frost can get under the shallow added concrete and push it up during winter. If you have serious frost conditions you would actually want to have the greater mass of concrete in the bottom of the post holes at a level below the frost line to prevent heaving and destruction of your fence.