By careful selection of the resistors its should be more than possible using your own suggestion to use a section of an LCD shield code.
Included a link to such a sketch so you can see how its done.
This already reads 5 buttons so another 3 would be quite simple.
It also includes a schematic from which to deduce your own resistance ladder.
I have used a similar approach in an industrial application and the only thing I changed slightly was to add a better debounce function with no loss of responsiveness.
If you strip out the unwanted LCD sections you are left with a quite nice sketch to add in your own uses.
A simple search of the forum itself also turns up a plethora of similar sketches and answers one such HERE
Or a slightly better method HERE with room to spare for additional buttons.