I tried "monty" myself when I was playing today's puzzle, but when it wasn't allowed, I accepted it meekly.
However, since you've brought it up, B-B-B, I have to look into it. I must say, I'm a bit dubious. The phrase "the full monty" has certainly entered the language, but is the word "monty" ever used in that sense without being part of the phrase?
Google does find a few uses of the phrase "the whole monty", but maybe that's just people who misremembered the idiom. You can also find "full motny", but that's not part of the language, it's just a naughty spelling mistake.
The only word list I could find it in is one called RIDYHEW (the Ridiculously Huge English Wordlist), but I'm not sure how reliable that list is.
Does anyone else have an opinion about this one?