Looking at Acts 7 and Hebrews 4 (plus their contexts), comparing these passages to the OT passages in view - and it is obvious that these two NT passages are referring to Jesus - Joshua just does not fit what is in view.

I would have to restudy out Acts 7, because I cannot remember offhand how it fits Jesus and not Joshua. However, Hebrews 4 states this:

Hebrews 4:6-8 Seeing therefore it remaineth that some must enter therein, and they to whom it was first preached entered not in because of unbelief: Again, he limiteth a certain day, saying in David, To day, after so long a time; as it is said, To day if ye will hear his voice, harden not your hearts. For if Jesus had given them rest, then would he not afterward have spoken of another day.

This is a quotation from Psalm 95, which was written by David, which we know was inspired by the Holy Spirit, the Spirit of Jesus as the NT refers to in a few places. The "he" in verse 8 refers back to the speaker - either Jesus or Joshua. Joshua didn't speak through David - but Jesus did.