Spiderwebs do not make a hot engine. The peehole is just an indicator that you have cooling water going through the system. If at first it does not come out but only after a while and it is real hot, you should check a few more things.
If it is an extra long shaft you should not use the muffs period you must put it in a barrel.
Did you put the hose on full blast or just a trickle because the water was coming out the sides of the muffs?
Did you put the muffs on the right spot or a bit off to the side? (sometimes when you turn on the water the muffs slide away a bit)
Did you check if any water came out from the outlet from behind the propeller? And was it hot or cool?
My worry is the thermostat. When you just start up the engine , there is no waterflow to the block until the block is hot enough to open the thermostat. Until then there should be cold water coming from the peehole and the through the propeller exhaust outlet. If it only lets the water through when the engine is hot then you have a blockage at or near the thermostat.
If it was my engine , I would check both the thermostat and the impeller pump and housing,and make sure that the hose os on full blast even when the water leaks around the muffs.
One last thing. Does your engine have a place to attach the hose higher up above the impeller? This is often there and it is to flush the engine innards after having been in salt water. If you do, screw the hose in there and give it full blast. If everything is open, you should water coming out of the peehole. just make sure not to run the engine when you this or you'll ruin the impeller/pump.