Hi...Smart and others are best to advise you on food. As for Xena and her jumping the idea of less people at once is a good idea. personally I dont and wont use a prong or pinch, but that is just me and do not judge others who do. I prefer to use more of a treat based method. How is Xena with her sit? When approaching a new person will she sit first before being stroked? Will she stay in a sit if you allow her to nibble treats from your hand? You keep a loose closed fist around a chunk of cheese or chicken say, let her be able to smell it and take little nibbles from it but not have it all at once, the opening of your hand should be just big enough for her to get her nose it and be able to nibble but not scoff. While she is in a sit then and only then do you allow her to be approached and stroked. I would try and discourage people from just walking up to her and giving her the chance to jump on them, she needs to learn her greet manners first before that can happen. Once she has clicked that sitting gets her treats and strokes then you can try a go the step further will greeting without treats but still from a sitting position. Dont allow her to jump on you at home either, the no jump rule has to be applied at all times. If she does jump at you at home then take her paws when they are on your body, apply light pressure, enough that its not nice but not hard enought to cause pain and walk towards her so she has to walk on her hind legs backwards...and with a firm voice say NO! Walking backwards on her hind legs is not natural, she wont like it not will she like having her paws squeezed. Failing that you can try the pennies in a bottle. Get a single serving sized water or coke plastic bottle and put some pennies in it. Invite someone over to your house and as soon as she jumps on them you throw the bottle on the floor and with a firm voice say NO! The loud sound of the penny bottle and the NO will shock her, she wont like it, and will be off that person in a flash. Do not look at her for a minute and then carry on as normal. Do not let her see you throw the bottle, its the noise she needs and you dont want her seeing that it came from you, this may instill a fear. I did this with my Akita once and never had to do it again. It may upset you to do it, it makes a huge noise, but needs must and a penny bottle, IMO, is much less comfortable than a prong collar. You may also like to get a Martingale collar for when you are out as well, this will give more control than a standard flat but not a harsh a choke, pinch or prong. IMO there are always other methods to try before one of these other tool collars but these methods are not a quick fix and can take some time and patients is required.
I'm confused about which dog is having the poopy issue, or is it both? You say you have only had Xena for 1 month, and that she is 10 months. She probably needs a bit more time to adjust to her new home and owners. I would try and not use the choker with the "spikes"....my own opinion. Maybe take her "quieter" places until you and she have more of a rhythm going. Maybe only socialize her with 1-3 people at a time, and build up. Just some thoughts 
