ribbon tweeters

The speakers in question are Mission 770, that I picked up for a song

Jeeez, I thought you were referring to Martin Logan (mentioned in yr "system")!!
Of COURSE you can play around. Hi Vi & B&G could be (cheap) contenders -- for a more expensive (real) ribbon you can check out offerings at Madisound & Zalytron.
You must find the xover's hi-pass frequency & filter slope & the present tweets' impedance (at the xover frequency -- or the nominal one).
The most difficult part will probably be fitting the new tweet to the opening...

Ribbons cross over at a higher frequency due to distortion limitations. This is one reason that you see many ribbon "supertweeters". Domes typically measure better mainly because of the distortion at lower frequencies. So your crossover would need to be changed, a resistor added or value changed will not cut it. Also the Hi Vi are not very good ribbons compared to the BG neo3 or the Fountek, Aurum Cantus etc.

The best thing is to run ribbons together with a dome tweeter.This gives the best of both.I note Dali is now doing this.The ribbons sound best above 7k.Try using just a 2.2 mF cap for an 8 ohm ribbon and sit it on top of your speaker.

JT