Hi gashby, (I had to correct stupid AI from calling you "dashboard")
You didn't say what year your 50A outboards are so I selected 2007 and newer parts pages for reference.
Did the larger tube come with a fitting with a larger nipple that screws into the block? (Item 9 in link below).
With that fitting removed and the leg of the outboard submerged in a trashcan full of water, you can try using a stiff wire to probe and~sort of dig n poke~ at any blockage in that passage.
The waterpumps on these outboards are very powerful and can push out things that tend to get stuck. Running the engine after probing/digging, with that fitting still removed, will often clear the passage completely.
You need to take precautions though because the debris can come out with great force followed by a GUSHER of water most are not ready for!
So, you'll want to do that in an area you won't mind getting soaked and be ready to instantly shut the engine off. Maybe even use the kill switch.
Beyond that, the fact that the stats were removed indicates other issues.
People take them out when they can't correctly resolve an overheating problem and that often means repeated overheats have taken place already. Luckily, these engines are equipped with fail safe protection systems that help prevent/minimize damage.
If these worked in salt water, there could be significant buildup of salt and other minerals in the cooling passages.
Many people use vinegar, in solution, to run through the system and break up those deposits. But, if the blockage is significant, it sometimes requires removing the water jacket cover (item 12 in link above) and physically removing the deposits as best you can. Note items 30 and 4 underneath that cover. The sacrificial anode and it's retaining screw. Those should be renewed while in there.
This engine utilizes several of those anodes inside the cooling system that might need replacement. Always replace the screw with the anode as they are small and can sieze.
In addition to deposits in the water jacket and engine block, the cylinder head can suffer the same and sometimes needs to be removed for cleaning.
DIY cleaning can be effective along with the vinegar flush. But if the deposits are significant in passages not accessible, complete engine disassembly and placing the block and cylinder head in a commercial "hot tank" might be required to completely restore those items.
I'm not a BF50 guru. I've never actually worked on one but I know my way around the parts pages and will try to help any way I can. Don't hesitate to ask questions because there are others on this site that know way more than I do. It's just that many are doing summer things and may be slow in answering.
Welcome to the forum.
Good luck.