Lost-causes, try, for a moment, to accept the premise that 1) metal detecting is not inherently damaging. Not during the recovery phase (that nasty 30 seconds of probing and prodding), and not afterwards (no sign of your presence left), and put aside, for a moment, the slobs in your mind who have left divots and messes, and 2) put aside in your mind, for a moment, the concept of goodies "taken" from the park (whether or not "
intentionally" looked for, or just
incidentally eyeballed).
If you can get those 2 mental blocks put aside for a moment, that no one cares about "priceless" clad and the occasional merc, and that you & I will be neat and non-destructive, then I do believe that THEN, you can see, that this activity would no more need permission, than someone swinging from a tree-branch would need permission, someone flying a kite, hopping backwards on one foot, someone "geo-caching", or any other such usage of the park. Now I know that you have a hard time believing that md'rs don't destroy things, and I know you have a hard time believing that the average person doesn't care if you find a ring or a coin in the park. And I know you have a hard time believing that the average md'r doesn't try to re-unite class rings, wallets, and other identifiable objects, but I do have an easy time envisioning those things. If something is found shallow (like the expensive prescription eye-glasses I found a few weeks ago: a fresh loss in the sand) I even put on Lost-&-Found on Craigslist!
So please, if you can get those pre-conceptions dismissed, you can see, that no permission is needed, anymore-so than any other use of the park.
If the "code of ethics" tells people they need to get permission for public lands where it's not currently dis-allowed, there will be some (a LOT in my opinion) that will start to actually create rules, to "address this pressing issue". Why would we want that? If it's not disallowed, and no one currently cares, why would we ask?
I come from a time (mid to late 1970s), before any of this nonsense started. When I started, as a jr. high kid, we would just put the compass 77b, and the Whites 66tr, into my friend's dad's car, he'd take us to the local old elementary school, & drop us off on a Saturday morning. Then he'd return after lunch and pick us up. Then when I got my driver's license in high school, in 1980, we expanded out to park and school yard hunting at a variety of nearby cities. Life was grand. No one cared. Yup, you just waved to the gardener, and went on hunting away in full view of street traffic. You see, it never even OCCURED to us, in those days, that "permission" was needed. Topics like this would have had us scratching our heads saying "huh?" I mean, afterall, it's public isn't it? It wasn't that we thought something might be amiss, it was just that it wasn't a thought that had ever occured to us, to begin with.
Flash foward to the mid 1980s. By now, we had a brick & mortar club of 20-ish to 30-ish members in our city. Our club started getting the FMDAC mailers each month. They were read aloud, and circulated about. Believe me, this was the FIRST time any of us had ever heard of such things. Ie.: accounts from somewhere else far away, of someone getting booted, fined, etc.... I can still vividly remember the hushed fears and resolve to fight (send in $$, etc...). But what happened next was this: someone in our club, apparently in response to these stories, and the "get permission" mantra (which they construed to apply to public parks too) went to city hall in our town, and asked "can I metal detect in central park?". Some desk-bound clerk told him "no". The next meeting, he raised his hand, and objected to someone's entry in the find-of-the-month-contest. The finder had been showing an old coin that was "found in central park". The new guy raises his hand and says "I thought it was illegal to metal detect in central park?" The rest of us just turn around, look at him, and say "since when? who told you that?"
Do you see what happens? If it was so "illegal", why had the rest of us gone there for years, and never had a problem

Mind you, it wasn't that we wouldn't have "asked", it was only because it had never occured to us, that "asking" was needed in the first place (having come from a more simpler time and generation). So what "changed" in this case? The mere introduction of the FMDAC mailers! Not that there's anything wrong with their stories and goals. But the unintended result of that was, that it began to be a self-fulfilling prophesy, so-to-speak. As people hear these things, they think that they too need to go ask, in places where it was never disallowed, and no one ever had a problem before. Ie.: "just to be sure", etc... And then it just spirals downwards

You get "no's" where no one ever gave the matter thought before, simply because maybe they think you're a geek with a shovel. Or maybe just because the mere fact that you are standing there asking them, just implies that something must be wrong with it, to begin with (lest ....
WHY would you even have to be asking them, to begin with?) Oh, and be sure to use words like "dig", "treasure", "archaeological resource", "holes" "ARPA and indian bones", etc... lest they not get the full mental picture.
Aaarrgggghhhh