Well, I'm a bit of a firecracker who works in a male-dominated field and this kind of thing angers me greatly.
The warden is different than your bosses, right? Does the warden work for the company or outside of the company?
In your situation, I'd come up with what I wanted to say and then I'd either send a letter/email to the bosses or ask them for a meeting to discuss. Whatever is more appropriate for your work culture.
I'd ask them if the warden also planned to ask people with limps and injuries to stay behind and let faster people pass. What about short men who wear lifts in their shoes? Are they slow? What about tall men who have dress shoes with a slight heel? What about someone who has metal pins in their knees and has had surgery? What about women who are fast in high heels? What about platform heels versus pointed high heels? Are they suggesting that I should wear dress shoes that are flats from now on? And I'd be very serious that it's very sexist and insulting that only women in high heels can slow people down, but men and/or women over the age of 60-65, or young people with rheumatoid arthritis cannot slow others down.
That if the warden were really concerned about speed, he should have said "slow people, please, move aside and allow faster people to pass. Or remove your shoes if they are slowing you down."
I'd talk to my bosses first and say it's insulting that they call you slow because you have high heels. And that if it truly is going to be a matter of safety, then they should not make it "very clear that heels are the appropriate corporate footwear for women."
Of course, I, personally couldn't work in an environment where I was expected to wear heels, not just dress shoes that are flats, nor would I work in a place (not saying your work is like this, but my friend's law firm is) where women are expected to wear skirts not dress pants. Those things, in and of themselves, I find to be very discriminatory. Why must I show my legs at work if men aren't expected to? But that's my tangent.
I'd start with the bosses, and if they ignored me, I'd either write to the warden or proceed with the government department. The only reason I might not talk to the bosses or the warden first would be if they would then pin me as a trouble-maker and it would affect my job. In that case, I'd just go straight to the government, and meanwhile be looking for other employment because I wouldn't continue to work in a place where I was looked at as "lesser than" because of my anatomy.