Well, this particular engine might be in pristine physical condition due to lack of use because it has been a problem child since new. The 74-76 9.9-15s were not OMC’s best efforts and had several update kits to improve running problems. All that being said, I don’t want to just condemn your engine because it is a 74-76 9.9hp.
Like everyone says, start with simple stuff. Compression, spark, etc…. The engine sounds like it is running on two cylinders, just dying out due to lack of fuel, but start with new plugs gapped at .030". The last time I knew, these engines used Champion UL-81J spark plugs, I have never tried the NGKs, but guys swear by them. Perhaps the fuel pump is weak, or there is an air leak in the inlet side of the fuel system. You mention using an old tank that appears to be unvented. Pump the fuel bulb up hard before starting the engine, then have an assistant pump the fuel bulb while it is running. A fuel supply problem is indicated if the idle improves using this method. Please do not attempt to rebuild this fuel pump, there are many tiny pieces that are tough to reassemble properly.
This could be a carb synchronization problem, a throttle plate that is not closing properly/improperly adjusted/partially stuck open would cause the exact running symptom you are experiencing. These early engines had some funky lockout linkages that were connected to the throttle butterfly, I have seen many that were stiff causing the throttle plate not to close fully. Someone may have messed with the synchronization and messed it up as well, causing the throttle plate to be held partially open at idle.
You have had this carb apart, and it looked clean inside. Generally speaking, these are pretty rugged/simple carbs, but it surely is possible to have a plugged idle passage that can only be investigated by removing the welch plug. This is not a difficult operation, but the mixing pocket is very shallow, so extreme care must be used when drilling through the plug. The simplest way to rule out carb problems is by just trying out a different carb on the engine, but I am assuming you don’t have access to another carburetor.
You may have an intake manifold problem, bad gaskets, or broken/bent reed valves. Does it look like the intake manifold has been off before, do the bolts look tampered with? I don’t recall upper/lower seals being a big issue with these engines, but anything is possible. But, like Casey says, you would probably see evidence of oil drooling down under the mag plate if there was a problem.
You mention that you just bought this engine, so I am assuming it has never run properly for you, is that correct? Did you get any service history when you bought it?
Remember, stick to the simple stuff, most problems are simple until we confuse things by digging into bigger issues and creating more confusion. You have picked a real challenge for your first project!

Well, borrowing your brother’s carburetor would answer a lot of questions quickly! Changing the carb is kind of a pain, cuz you need to move the manual starter out of the way to get at one of the carb retaining nuts. Once the manual starter is loose, thread a 3/8 wingnut onto the thru bolt to hold everything together. Do not pull the thru bolt all the way out of that starter, there is a spacer/washer inside that you don’t want to dislocate. Be sure to get the starter cup locating tab back into its hole on the manifold during reinstallation as well.
And yes, there isn’t much movement in that mag plate when in neutral. But, there is an adjustment on the shift lever cam that will allow you to raise the neutral speed limit on this engine. Look on the right side of the engine where the shift lever connects to the shift detent cam, you will see the limit/stop that is retained with two screws. Simply loosen the two screws and move the stop forward to increase the neutral speed limit.
The throttle cam/carb sync isn’t too tough to do, I know it would help if I could provide some pictures. The thing to remember here is that the throttle plate on these engines is completely closed when idling. Look on the mag plate throttle cam, you will see a raised mark/arrow. Basically, the carb butterfly/throttle plate should be completely closed until the raised mark/arrow is in the middle of the carb throttle plate roller pick up. Unfortunately, the adjustment on this engine isn’t too easy because one of the cam retaining screws is sandwiched between the flywheel and mag plate! A quick test is to look at the throttle roller while the throttle is in its idle position, the mag plate throttle cam should not be touching the throttle roller. Slowly advance the throttle, the carb butterfly should just start to open when the raise cam mark is in the middle of the carb butterfly roller. Don’t get worried if the throttle plate starts to open only after the mark passed the middle of the roller, this will only cause a rough/rich off idle situation, which is not what you have going on. A carb butterfly that opens too early, or is still partially open at idle will spit/stall like your engine does. Keep in mind that just because the roller is not touching the cam does NOT guarantee the throttle plate is completely closed. A weak butterfly spring, or worn throttle plate could hold it open slightly. Your engine also has a recoil lock out that is connected the throttle plate roller linkage, this could cause the butterfly to be held open as well if things are stiff. Unfortunately, the only way to ensure the butterfly is closing completely at idle is to remove the carb and look at throttle plate movement from the back of the carb.
There is no way of telling whether the reed valves are broken/not seating properly unless you remove the intake manifold, let’s leave this for a later step if your brother’s carb doesn’t improve things and you don’t find sync/linkage problems.

quote Garry in Tampa:

It will foul plugs if the thermostat sticks open and the engine runs too cold. This can happen if the water pump fails and the thermostat gets hot enough to blow out the expansion jell that it uses to regulate the opening. It should normally run around 145 degrees Fahrenheit. The thermostat used opens around 140 …

Garry makes an excellent point! Once again, don’t skip over the basics, simple stuff!