You could argue that it's worded poorly because it's not worded like the designers wanted (as evidenced by Mearls tweet) and I wouldn't argue that. But as it's written, it's clear. Any time you say something "can't be below X, or it is X", that means it's the final check in the process. It's a simple IF-THAN statement that's been around since before the days of BASIC coding. Nothing about that spell triggers until the AC is below 16 when tallied. Even if you were to argue that that check is made at every step of the process, you still wouldn't ever have an AC over 16 with that spell
For example, if you cast the spell and your AC is 14, then it triggers the spell and your AC becomes 16. If you then add a shield which brings it to 18, then the spell no longer is in effect since it's not below 16, and wouldn't take effect, which means you'd be back at your base 14 +2 for shield = 16.
That's because the spell does not take effect unless your AC is below 16, RAW. Again, it might not have been intended that way, but RAW, that's what it means. And in plain English, that's what it means when you say that "if something is less than X, then make it X."
Another example.
Let's say you make $1000 a week for 40 hours of work. If you have a rule that states if you work less than 30 hours, your minimum pay is $750 a week. So let's say you work 23 hours. The rule kicks in and you make $750. If you then work 10 more hours in that week somehow, that doesn't mean you get the $750 + the additional pay for the additional hours because it's inferred that that rule isn't checked until the end of the week. Just like the barkskin rule, RAW, doesn't take affect until your AC has been tallied. That's what that language means, and that's how it's used in logic when programming.
I'm also not ignoring the "regardless of armor" because that's a redundant statement. By your logic then, it means that it ONLY factors in armor since that was the only thing expressly called out. Does that mean you're arguing that barkskin is stackable with DEX, other spell buffs, magic items, and shields?