TL;DR: Grab the Nikon NIKKOR Z MC 105mm f/2.8 VR S. It fits your $1000 budget, fixes the balance, and native focus is way better than using that clunk...
Honestly i feel your pain so much! Making that jump to the Panasonic Lumix S5II is such a massive upgrade for video but the lens situation is definite...
Seconding the recommendation above! I had a similar struggle before a trip to Rome last year. The reach on the Fujinon XF 18-135mm f/3.5-5.6 R LM OIS ...