Well you are in luck. Have the panels off my 1811, so I snapped a couple pics.
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PLEASE READ/FOLLOW EXACTLY:
I have done this many times, on many different motors, and transmissions.
No, there is no way to get to the screen.
Pull the drain plug, go get a gallon of gas and a gallon of diesel fuel. Dump the gas down the motor first, that will wash it out. If it still looks nasty, repeat. Then dump the diesel and let it re-lube and flush the gas. Then, I'd dump at least a quart of cheap whatever oil down, and let that run out too. Then refill and start it. I'd also add sea foam to the oil.
IF you have oil pressure, let it run for a couple hours use, then drain and refill with just oil.
**CHANGE THE FILTER ALSO** That combo should clean out the gunk.
NOTE: For anyone changing oil. It is far better to drain oil out of a hot motor because the warm oil 1.) flows out better and more completely. 2.) has a better chance of pulling some of the "gunk" (if any) out with it because it flows out the plug faster.