Strange behavior of old cone tweeters

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I came across some old no name "Model 22" speakers a few months ago. The cabinets are so well made, I just had to get them. The woofer is a CTS and the tweeter is a Quam-Nichols. They are early 1970's,

When I first listened to them, they were OK, except for a strong midrange peak. I identified this as the 1400 Hz tweeter resonance. The crossover is a 4.7 µf capacitor on the tweeter, which should be around 4000 Hz. The reason I'm hearing 1400 Hz is likely the impedance being very high at resonance. I already replaced the capacitors.

While I was playing around with them a bit, I noticed I can almost silence the resonance by putting a finger on the dust cap. I duplicated that with some tacky putty I had lying around. I don't have a calibrated mic but I can use a program to see differences in response. A small amount of putty, .1g causes a notch in the tweeter response with everything below the notch being lower. At a point around .7g, the notch becomes the roll-off you would expect. No amount of putty affects the response above the notch and touching the cone anywhere else doesn't tame that resonance. So here is what I find strange. I have always been taught that tweeters need to be very light. I also thought that that the center dome reproduced the highest frequencies from a driver.

So what should I do now. I could buy some 2nd order crossovers or add a choke but that might cost as much as replacing the tweeters. Since I may replace them anyway, should I try removing the dust cap to see what happens and possibly replace it with something else? Should I leave the putty on the domes? Should I try putting small holes in the dome to see if it's an air cavity resonance? I'm honestly surprised at the brightness of these tweeters when it isn't being buried under a nasty resonance.
 
Are you sure it isn't just the dust cap becoming unglued? That's easy to fix with either glue or even if small enough some nail polish clear coat.

Anything more than that and I'd say replace the tweeter, but that's never just 1 part. 🙂
 
My connection is bad right now but here is one picture.
 

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