You need to backflush the intake line (hose) not the engine block. You may end up replacing the impeller, so don't rule that out.
The hose that is getting hot is the recirculating hose (orange). It sounds like not enough cool water is getting into the engine, because not enough hot water can exit the engine. Hot water has to exit before cool water can enter.
Back flush the intake line (dark blue).
Inspect the T-stat housing for rust and or clogs
Inspect the exhaust manifolds and risers for rust/clogs
Dark blue is the inlet water from the outdrive.
It splits and goes in different directions at the thermostat housing
light blue is cool water to the risers
Orange is warm/hot water recirculating from the top of the intake manifold to the engine block
Red is the hottest water exiting to the exhaust manifolds (and up into the risers).
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