Technically yes, it is possible to create a recipe which is preserved by both salt and sugar. But this doesn't mean that you can get any significant reduction in the total amount used (or, controversially, even in the amount of each).
That would avoid the overload of either sugar or salt.
No, it won't avoid it. You absolutely need such an overload to preserve the food. If you reduce the amounts to the point where you can eat it without it being too much for you, it won't be too much for the bacteria either, and the food won't be preserved.
Instead, the result would be a food where you get an "overload" of sugar and salt at the same time (which, to me personally, tastes worse than a high amount of either one on its own).
Remember that sugar is not really a strong preservative, so it always has to be combined with other methods. Simple syrup on its own is not shelf-stable; when you use sugar for preservation, you have to either combine it with drying (=candied fruit) or canning (=jam). So, in typical salt-based methods, you can forget adding a little bit of sugar; it may even make a pickle unsafe by providing more food for bacteria. You would have to achieve a really high concentration of sugar for the whole to work.
So you could try the opposite, adding some salt to the sugar-based preservation methods. But how are you going to go about it? When candying fruit, what you do is to saturate everything with a sugar syrup, then let the extra liquid evaporate. How do you suggest to reduce the sugar? If you make the syrup more diluted (because you now have the salt), this only means that you would have to wait longer for the extra water to evaporate in the drying phase, after which you will still have the same high concentration of sugar.
You could make jam with less sugar and add salt, but in fact, you can also make jam with less sugar and not add salt. Basically, what jam requires is a proper acidity level and a proper sterilization procedure, independently of sugar levels, that's why you can can vegetables in water just as well as fruit in syrup. So, by adding salt to jam, the only thing you have gained would be a changed taste, probably for the worse.
The commenters mentioned a few cases of real-world recipes combining salt and sugar. They were all recipes for cured meat or fish, which is a very different process from your plant-based example. I cannot tell you to what extent both ingredients are contributing to the preservation in these recipes, and to what extent the sugar is there for taste only (they are all salt-and-nitrate driven preservation methods, you cannot preserve meat with sugar alone). If you try them, you will note what I said at the beginning of the answer: they still use a substantial amount of salt and sugar, and the taste is very intense.