65 Barracuda daily driver
It sounds like everything is good with the new pump. There really isn't a good way that I can think of to run a wire or brush up into the oil passage that goes from the pump to the oil galley. To clean the oil galley's that you can get to, you would have to pull the engine, and then, at best you would just be pushing any sludge that you could dislodge around to another place. I don't think it would be worth the trouble, honestly.
Test fit the new pump to the main cap and make sure it is seating properly. Not sure if your motor will have one, but the rear main cap of my 273 had a hollow dowel sticking up maybe an 1/8th of an inch that the pump had slide down on, but it's the only small block that I can ever remember having one of those. Your new oil pump probably came with a gasket for where it bolts to the cap, so be sure and use it. You will probably use the new pickup you have when you put it back together, so check the pan to pickup clearance with some clay. Just tape up the screened opening of the pickup while checking so it doesn't get gobbed up with any clay if it squishes in that direction when you press the pan up tight to check. To make it easier to check while laying on your back, leave the end seals off the pan while checking. Tight against the block with pan rail gasket thickness is what determines the depth anyway.
If you get it back together and it still does it, just drive it and enjoy it while you find another small block (Magnum version would be my choice) to rebuild as you can afford to, and then swap it in when it's done. I've had a few that do the same as your motor does...being a slow poke to turn the oil light off at start up, and they lasted just fine. The oiling system in engines is just a controlled internal leak anyway....lol. You're doing a good job and I admire your tenacity in fixing whatever you have to instead of giving up.
:thumbsup: :thumbsup: