I've always been fond of the Boston Acoustics stuff. It's pricey, but it rarely disappoints.

I can't speak 100% to what Kortec is, but many manufacturers use different polymer based materials as a sort of "bridge" between a soft (ie silk) and a hard (ie metal) tweeter. They try to get that extra pop, while not making them fatiguing.

The Alpine Type-X is more of a... "goes with subs" speaker. IME the Type-R is more capable on its own if you will not be using a subwoofer.

Those Pioneers are pretty decent speakers for not a lot of money, they surprise a lot of people (I blame the aisle full of cheapo Pioneer gear at Walmart for that).

FWIW, I believe all of those speakers you listened to (except some of the JLs) should have had one of the "poly-soft" style tweeters. If you can, check out a set of the Kicker (DS or KS) components, they have a hard dome tweeter. Should give you a decent idea what to expect from that.