I can sympathize, since I have large hands. I usually need XXL gloves, and sometimes they fit tightly.

My two main solutions were mentioned above. Double wrapping or the foam. I don't care for the foam too much, but it is personal taste. The "cool kids" don't like it, but that doesn't bother me, it is just a feel issue. I do find that wearing padded gloves keeps the narrow bars from bugging me quite so much.

In addition, some tape is thicker than others, so seek out the thickest tape. It really does help. I don't know how we used to ride in the old days with that thin plastic wrap.

There are also gel pad systems that can be used to provide padding and thickness under the tape of a drop bar. I don't recall specific brands, and I haven't used them, but they exist and could be helpful.