It is definitely not tuned correctly regardless if it was at one time. You are probably flooding out from a dirty float needle/seat if you have a lot of black oily fluid dripping out the pipe. Gas is leaking down through the cylinder and into the exhaust. Everything you described points to that. Sitting for a long time, ran but now hard to start, having to hold the throttle wide open to start, takes a while once you start it to run decent, etc. Having to hold the throttle wide open to start is your engine needing and trying to get more air to lean out out the mixture.
Take the carb back apart again and re-clean everything and really focus on the float valve seat. The tiniest little particular will cause it not to seat and gas will seep into the engine when sitting . Never ever refuse spark plugs when trying to sort or or diagnose these kinds of issues. Often, plugs that have been fouled due to flooding or a rich running engine may be still causing issues too but may look fine to the human eye.
Re-clean the carb
Put in new plug
Clean and gap points.
Clean air filter
If possible, clean out exhaust
Run for as long as you can at high speed to clean out the engine...do not let it sit and idle for more than 15 seconds at a time.
If running good now, you win
If not, start the rejecting process by dropping a size. You can also experiment with the air intake flow by removing the filter temporarily and see if that made a difference.