Looking over your menu, which is varied and may be eaten in any order - how about serving just one wine?
The best choice to fit with everything, including dessert is champagne! Or a good prosecco for the budget. If you avoid the "brand names" some nice champagne (by the case) can be almost within your budget. And it feels classier. And no build up of tannins on the palate at the wrong time for the wrong course......
Just a thought.
If your budget will stretch, go for a Charles Heidsieck, whose non-vintage stuff has risen in quality to almost vintage levels but without the price....