While looking into CLOUDP-62356, I encountered the following scenarios:

EJSON.stringify({ intField: 222}) = "{ intField: 222 }"
EJSON.stringify({ intField: Int32{ value: "222") = "{ "intField": "222" }"}}
EJSON.stringify({ intField: Int32{ value: "222" } }, { relaxed: false }) = "{ "intField": { "$numberInt": "222" } }"

In the second situation, it seems like the desired output would be:
EJSON.stringify({ intField: Int32{ value: "222" } }) = "{ "intField": 222 }"
with no quotes around 222 like in the first example. Otherwise, it gets recognized as a string when passed back into EJSON.parse.