Can dry roasted squash be used effectively for gnocchi?
Some ideas:


I like to do do pumpkin gnocchi. The dryer the pumpkin, the better, since you will need to add less flour and get a lighter result. It has a lovely sweet taste compared to potato gnocchi and goes really well with sage and butter or blue cheese sauce. The recipe in the link is just suggestive. My approach is to add an egg yolk and to keep adding flour just to the point where the mix gets together. The reason is because the less flour, the better the final result (however flour is important, otherwise you get a sticky mess that you won't manage to roll and cut). 
Also on the pasta side, you can make ravioli filled with pumpkin and again serve with sage and butter sauce. 
Pumpkin bread. You could incorporate your pumpkin puree in a bread dough and proceed as usual for bread (you can do sourdough, tin bread, etc). The sweetness of the pumpkin works great when serving the bread with cheese, and the pumpkin gives a nice orange colour.
If you have not salted it, pumpkin sponge cake or pudding.
Pumpkin soufflé, goes well sweet or savoury.