I read through this whole thread looking for some comment on the late 50s Hegemann water lily tweeter which is very much the same design as the much later Walsh tweeter. Stu Hegemann of HK designed a tweeter with the same tall unterminated cone glued into a standard tweeter voice coil, but he used a piece of graph paper, and didn't bother cutting it into a cone -- it unabashedly looked like a cone made of graph paper. I believe he felt that the shape diminished the major resonance(s) in the cone, and he didn't feel it needed damping inside. The tweeter got good reviews, and Eico made a column speaker that used it in a similar implementation to the Monitor IIs -- open sides and solid top. This was all at the tail end of the mono era. Edwart Tatnall Canby of Audio liked it very much and gave it a most positive review, but he later noted that it produced too much top end in stereo -- the omni effect was nice in mono, but apparently too much with two speakers. I've been looking for a pair ever since I first heard of them, with no luck.
I bought a pair of Monitor IIs (maybe IIas, I can remember) at a tag sale fifteen or twenty years ago. The owners had replaced the Watkinson dual voice coil woofers at some point, and had stuck Radio Shack Linneaum tweeters in the front of the tweeter compartment. I can't remember if the the Walsh tweeters there worked or not, but what I do remember is that there were three pairs of the tweeters in boxes in the garage -- a couple open and the rest still sealed. So I bought the lot. The speakers were okay, but with the wrong woofers, didn't billow my sails (and the cheapness of the wiring and crossover components rubbed me the wrong way) so I sold them to a friend who parted them out, I think.
He also bought the Walsh tweeters and contacted John Strobhein (sp?) of Ohm to ask him about them and John bought the unopened pair because he said he was trying to figure out how to make more.
That was long time ago, and I have not idea what came of that idea.