You didn't describe your plants but let me allay your fears. The ground settled only by 1 inch. This is insignificant and shouldn't have a big impact on your plants. If you are concerned, simply remove the soil to the level you want, put barriers around the base of the plant to keep that extra soil from returning.

Shrubs & trees can be suceptible to rot at their base if planted TOO DEEP and the base portion of their trunks lies below ground. This allows bacteria, fungus and other pests to enter the trunk and affect the plants. Roses for example shouldn't be planted too deep.

As for other types of perennials like say echinacea, daylilies or basically the types that die back to the ground every winter. - Don't worry. This won't affect it. In fact, with winter coming, the problem would be that these new plants can get pushed outwards by the freezing and thawing process.

So, if you still feel troubled about the depth and still want to replant your plants - be aware that it's summer now and so wait until the plants go dormant in the fall before you do any transplants.

Last, I've described the approach to perennials. As for annuals, they are mostly shallow rooted and of course will die in winter. Annuals cover a wide range. Some can handle deeper soil coverage but some like balsam would probably rot if planted too deep. In this case, remove the extra soil, don't do any transplants as this will surely feel the heat of summer.

Ianna