There's massive interconnection between Joseph-the-type (we will not have this man to rule over us) and Jesus-the-anti-type.
I realize the NT doesn't give him "treatment" the way it does David, Abraham, etc. But that's no excuse for not taking what we learn from those instances--about how the NT would have us employ the OT figures--and applying it on what is (arguably) as obvious a test-case for expounding a type-of-Christ as can be found anywhere in the OT.
Here's just one
verbal connection, one I think the NT/HS meaningfully provides for us:
Mt.27:18 "For he knew that for envy they had delivered him."
Act.7:9 "And the patriarchs, moved with envy, sold Joseph into Egypt: but God was with him."
Joseph is the man through whom the Lord promises to bless his covenant people, Gen.37:7-9.
His own receive him not, Gen.37:8,20.
He is received back from the dead (cf.Gen.37:33 & 45:28).
He is exalted to the right hand of power, Gen.41:40.
The whole earth (Gen.41:57) is obligated to come to Joseph for salvation.
There is too much to reduce here. Just preach the text as Christian Scripture. If Joseph is no type-of-Christ, then indeed the apostle's interpretive grid is non-transferable to their teaching successors in the church.