I think bitters would work quite nicely here, as long as you have the right ones.
There are surely many good drinks that could be made with these ingredients, in varying proportions, with and without bitters. I am curious to try Lillet in place of Dry Vermouth in the Hong Kong Cocktail, perhaps reducing the sugar a bit.
So, maybe, 2/3 Gin, 1/6 Lillet, 1/6 Cointreau, with an orange peel squeezed over to make up for the lost orange flavor, an a pinch of Cinchona?
What I liked about the Campden was how the delicate-fruity-floral flavors played together. Going to 4:1 Gin to Lillet would change the drink a lot. As I said above, I actually liked it with a little more Lillet. In any case, drop the amount of Triple Sec and this is a drink worth experimenting with.
Pointing up Lillet by adding Cinchona bark, now that sounds interesting. I am no fan of the Vesper, at least not the incarnations I have tried so far. My wife described it as a "girly Martini", which sounds about right to me.