You should be okay, it's kind of hard to overfill enough to displace all the air due to the air space around the crankshaft gear, air will be trapped there. Some air space is necessary b/c the oil will expand as it heats.
After running for over a month, can you still see some oil? I expect it will be lower than the fill hole due to some oil has moved away into the crankshaft gear area, this is normal, it doesn't mean the oil has leaked out unless you cannot see the oil below the fill hole then add some until you can verify there's definitely oil in there.
I check mine beginning of every season and top it up if I can't see oil, this way I know for sure there's always some there.
Keep an eye on the level if you think the reservoir is leaking, the gears must always run in an oil bath.