It can be tricky, but the EMIT diaphragm can be replaced. Orange County may have some in stock. These were sensitive to extreme HF oscillations, like what occurs when an amp clips badly and have seen several that looked like a blown fuse at the point of failure.
If the tweeters came on briefly, look at the crossovers. I have seen crossover caps that blew apart from excessive voltage and they often use caps with a voltage rating that's too close to what they can be exposed to in normal/abnormal use.
The new sound definitely could be from bad alignment. If the dust caps were removed or came off at some point, it's likely that there's something in the gap. It's also possible that the cement holding the spider has let go.