Daryn, ok, to analyze your post line-by-line:
a) now that you've told us they are crown caps (and not screwcaps) that are bedevilling you, me thinks you're not using your machine right. Most machines can reject those. If it's true that the 350 is letting them come into any of the conductive categories (even after setting it for "bottle cap reject"), then here's the next step to take: Crown caps (ESPECIALLY RUSTY ONES) will have a very tell-tale audio difference when you alter the sweep speed. They tend to "break up" when you momentarily speed up your swing clip over the spot. Contrast to if it's a coin (or some such conductive target), and the signal will not break up with altered/varying swing speeds. Of course this assumes you've got your target centered good (because it can also "break up" if you're not centered over the strongest spot). Once you're getting your signal clearly on each swing, then speed up the speed to a fast little "whip". If it breaks up, then it's likely a crown cap. Practice a little, dig a bunch after comparing audio, and see if this trick works. This trick was VERY pronounced in the early days of motion discriminators (late 1970s/early '80s). However, the swing speed has been slowed way down. Yet the "trick" is still there, to a lesser degree, but can still be used.
If that doesn't work, then I'd say the 350 is a lame machine and time to upgrade. Because on most machines I've used in the last umpteen years, crown-caps are easily learned and passed (if you so choose to be that picky, that is).
b) If you're digging 100 targets, of which 20 turn out to be coins, and the oldest of them is "1971", then ..... I'd say you have a lame spot (unless you're really turned on by clad). I can go out and dig 100 targets, and have every single last one of them be a coin, if I wanted (if I chose to be that selective). Maybe interupted only by a car key, brass washer, or something coin-like. I suppose though, that you are in low disc. (and thus digging every last tab, foil wad, etc.., right? Or were you in high disc?). If so, then are you trying to be a hero and find nickels and/or gold? If so, with ratios like that, I'd say this is not the environment to be a hero like that (unless you just enjoy digging junk).
The "dig all" relic-mindset is for the beach, or relicky sites (old town demolitions, ghost towns, ruins, etc...). But at junky inner city turfed parks, I'd go for the old coins. Oh sure, you can be a hero and try to get gold jewelry, but .... there are parks that your average will be 1000+ before you'll ever get a gold ring. You'd be much better off to cruize all the sand boxes in your town (or find a swimming beach) if gold is your desired goal.
Or if you really must hunt turf in your quest for gold jewelry, here's another idea: turf that is/was used for picnicking is bound to be MUCH more junky, that turf that was/is used for athletics. Because anywhere that people eat, they're going to disgard foil (foil that wrapped their food, candy, etc...) and tabs and caps (from sodas). And with BBQ pits, there'll be molten globs from people who put their cans on the fire, or cooked in foil, etc.... HOWEVER at athletic fields (soccer, etc...) they're not typically used for people cooking food, sitting at picnic tables eating, etc.... AND they are SPECIFICALLY used for physically aggressive "frolicking" motion (athletic) activities. That bodes much better for jewelry coming off and being flung, dis-lodged, etc... Some turf doubles for multiple things, I know. But if you know of turf that's *strictly* for athletics, your jewelry vs junk ratio will be better.
However, still not as good as swimming beaches. Because the very nature of swimming is the most condusive for jewelry losses. Cool waters shrink fingers. People lathering up with slippery suntan lotion. People thrusting their hands into sand which affords a "pulling" motion on their fingers (pulls rings off). People lying prone on the sand (an un-natural position, as opposed to the normal standing position) to sun-bathe. And my favorite: People taking off their jewelry for "safekeeping" before they swim (and hide it in their shoe or something

). And of course: sand is easier to dig in.