Well, that’s incorrect, then. The principal runs your school, but that’s because he’s the principal administrator. He may also be principled, but that’s a separate issue. You can also say something like “Working hard to provide for my family is my principal principle in life.”
Well, I think it’s settled, so I don’t have much to add except that obviously this “very smart” colleague isn’t as smart as you thought, at least in terms of his vocabulary. This is not “regional” usage, #1 is wrong everywhere, #2 is unambiguously correct everywhere. And as a Canadian, I speak a sort of hybrid of both US and British usage and am familiar with both.
Of course it would be correct to say “there are three principled reasons for this approach” but that’s a completely different meaning, and a rather awkward sentence structure. To convey that meaning, I’d rather say “the reasons for this approach are based on three principles …” In any case the point is that “principal” and “principle” have completely different meanings – everywhere.
It seems like it’s a matter of principal…
Runs away
But the OED also marks this usage Obs. (obsolete), the most recent cite given being in 1823.
Since the OP’s dispute is explicitly over a British usage, the OED would be a principal reference for OP to cite. It would be hard to find a more authoritative source than that.
How is principle a verb? Is there an example of its usage as a verb?
Or you could substitute ‘principle’ for ‘rationales’, ‘reasons’, ‘sets of reasons’ or ‘fundamental reasons’. Personally I prefer “There are three fundamental reasons for this approach…” as a nice hook, although I don’t know the context and you sticking to ‘principle’ could be more suitable.
(English) English teacher
I totally agree usage 2 is “right”, but not really correct. Having multiple “Principal reasons” conflict with the meaning of principal, in this case. That’s like saying “A unicycle with two wheels”.
Or “more unique”.
No, that’s an overly restrictive interpretation. The adjective “principal” can properly apply to a plural noun, not just a singular. Indeed, the online Oxford dictionary offers “the country’s principal cities” as the first example of usage. Another dictionary has “vegetables are the principal ingredients in this soup”. “There are three principal reasons” follows the same usage and is unequivocally correct.
I was taught that the initial drawdown for a mortage is the principal…
That sents a princi… a precedent…
perhaps money is my friend, but its not likely to be called my pal…
When principal is used a noun, such a principle is the original or first or most important thing (or things, for the pendants, that is also correct. yes you can have three three principals at your school, you can have three principal reasons too … )
Principles are always nouns but they are ideas… certainly not people or amounts of money.
I think you mean pedants.*
You’ve probably seen it as an adjective, as in “he took a principled stand.” You need to go through a participle (i.e., verb) form to get there.
*This one is actually ironic, not Alanis ironic, right?
That’s exactly the route I went! Are you reading my documents? 
I feel vindicated to have gotten this right. However, an odd twist here… in the company documents, I’ve found numerous occurrences of ‘principle’ as an adjective from multiple authors going years back. I wonder if this is a misuse that will someday be considered normal in the UK.