Is it possible to have one field become mandatory based on the values in two other picklists?

Then you would do a CASE like this = 

AND(
    CASE(
        StageName,
        "3. Proposal Development",  1,
        "4. Validating",            1,
        "5. Securing",              1,
        0
    ) = 1,
    TEXT(Type) = "New Business",
    ISBLANK(TEXT(Product__c))
)