In Taiwanese, what can the erhwa be replaced with when it means something?
In my experience 儿 doesn't really perform the role you mention about changing a verb into a noun, it just reinforces that something is a noun when it's ambiguous. For example 画 is 'to paint' or a painting, so if you mean a painting you say 画儿 to be clear you don't mean 'to paint'. But 吃 doesn't mean food, it means 'to eat', so 吃儿 doesn't need to exist to distinguish the two.

In Beijing I've found that most of the words with extra 儿's at the end are nouns that sound like other words. Adding the 儿 reduces the ambiguity when speaking by reducing the entropy of the language. That being said, there are lots of exceptions, 玩儿， 那儿， 这儿 etc.