As far as doggies, poodles IIRC and definitely Yorkies are for those with allergy problems- they have hair compared to fur.
If fructose is in, you will just have to experiment with juices- though I suggest concentrates from health food stores, you avoid having to cook down water to thicken it up. Absolutely no ketchup (legal definition requires % of sugar), you will need to check tomato sauces if you go that route or vinegar base as mentioned- typically the vinegars include mustard IIRC.
My suggestion to for starting off with substituting juices is to look up Caribbean Jerk recipes, I will have to check mine at home but it has OJ, fresh squeezed lemon and I add limes at time. Look at the meat/portion to juice ratio and you should be able to figure out how much you need to get it to work as sweetener. One other thing you might consider is looking at diabetic or other special diet recipes-
https://www.diabetes.org.uk/guide-to-diabetes/recipes/jerk-chicken has a smaller amount of sugar than other recipes I spot checked, makes it easier to substitute.
Another possibility is using stuff like raspberry-habanero preserves as a component. Not jellies- IIRC they use lots of sugar. Preserves have the highest fruit ratio, and again you lose a lot of the moisture from a juice that you would need to reduce. From what I can quickly find, berries are usually best for sugar-free preserves- it mentions blackberries, strawberries and raspberries in particular.
Hmm, I might have to sneak some raspberry-habanero preserves into the caribbean jerk recipe next time.