I'm very sorry your Gina has escaped.
Have tried to find her by posting flyers on your neighbourhood, closest vets/pet stores, contacting your local animal shelter? Advertising online can also be helpful.
While I do understand your concern over Jack, it's always recommended to follow quarantine measures before introducing a new budgie.
In cases like this one, having the new budgie checked by an avian vet specialist would have been the best course of action and depending on how the wellness check went, you could then break quarantine and start the introductions.
If the bond you have with Jack is solidified, you shouldn't expect a big setback on his taming. Since the new budgie is still very frightened of you, you can continue on working more closely with Jack in terms of training by spending one-on-one quality time with him.
As for your new budgie, it's best to take things slow and for now to make her used to your presence and voice by talking in a calm, positive, encouraging and reassuring way. Once she shows the first signs of being more curious and receptive to you, that's when you can move to the next step in training by slowly introducing your hand and offering her a little treat to eat through the cage's bars. By watching her body language and respecting the safe boundaries set by your budgie, you will know when to proceed.
For all the detailed information and tips on this subject, be sure to check the stickies at the Taming and Bonding section.