Lens caps are for use on lenses that are in storage. They are not meant to be used on lenses that are in use, such as when attached to a camera. As you have experienced, they are not particularly resilient, they are easily detached in the field, and they are easily misplaced.

In the environments you describe, city and museum walks, obsessive use of lens caps is more likely to damage the lens than simply leaving them off, especially after they are likely to have picked up grit after being retrieved from "sidewalks or in the sand or bushes".

Attaching matchsticks to lens caps and gluing lens caps to lenses seem likely to be counterproductive. However, you do have several other options:

• Obtain inexpensive lens caps from China. A lot of 10 costs ~$8. (Hurry, before tariffs set in. Although not everyone is in the US, you do reference the Nikon USA store.)

• Use transparent lens caps (aka, "UV" filters). They cost a bit more than ordinary lens caps. Make sure it is multi-coated.

• Use neoprene lens caps, which Chris H mentions. You can purchase ready made "LensCoat Hoodies", or DIY from a bottle holder.

• Some people use lens hoods to "protect" their lenses. How well this works depends on the specific perils your equipment faces. Lens hoods should be sufficient for city strolls and museum walks.

• Use cap keepers, as osullic suggests. However, some find that a cap dangling from the lens is annoying. Looks like a pack of 15 costs less than a pack of 5?

• Purchase your own photography gear so you won't be subject to the whims of others. By having your own equipment, you also avoid damaging others'.

• Purchase only a lens so the current lens can be safely stored away with its lens cap glued on. Yongnuo has some inexpensive prime lenses that may be worth trying. (I have not tried any.)