Second, and more mysterious -- perusing places like Home Depot, it seems like support pegs are usually pretty standard. But I can't find any that fit our cabinet! The design of the peg is unusual, it has ridged pegs and doesn't seem to be a normal size. Unfortunately these were installed by a previous owner of the house.
I took pictures of one of the pegs from different sides. One pic is attached with this message, but all three pics can be seen here: https://www.screencast.com/t/E25DR2a2B8l. If it looks at all familiar to you and you have any leads, please let me know! Many thanks!