Tripoli is horrible. Talk her round please!Elisabeth is the better spelling. It is also more representative of the original Hebrew form: Elisheva. Elizabeth only became popular and the norm because of QueenElizabeth I.
I still like Elizabeth better. And in your opinion Elisabeth is better, and I think Elizabeth is. That's fine with me. And frankly, you could recognise Elisheva in Elisabeth no more than you could in Elizabeth. If you want names to be just like the original, I say use the original.