When I said earlier that, when preceded by a numeral-word, 'foot' could be used effectively as a plural, it wasn't just me making it up...it came directly from The Oxford English Dictionary - the 'bible' of English word-usage. One of the earliest quotes the dictionary uses in illustration of this fact dates back to 1205.
The plain fact is that saying, "I am six foot one" has been perfectly acceptable for centuries. In fact, I cannot imagine anyone saying it any other way, although "I am six feet one" would not actually be wrong.
We are all aware that the standard plural of 'foot' is 'feet' but, in English, usage is king and if we've employed a usage for nearly 1,000 years, it's fine to go on doing so.
If you've arranged to call on someone and you go and knock on their door, they may well call out, "Who is it?" You are perfectly entitled to reply, "It's me", even though the 'correct' answer would be "It is I." Why? Because that's what virtually everybody - with the possible exception of a professor of linguistics - does say!
Stick with "six foot" in these circumstances, BB...trust me.