I am currently weighing something similar, though not as cushy as the one you are in.
As I'm nearing negotiations, I'm looking to see how I can do both, at least for a few months.
If you left the current spot, is there a pay cut?
How long can you do both, reasonably? Do you have vacation/sick days that you can take? On my end, I have about 4 weeks that I could take, which guarantees the pay from both jobs, but, also, I wouldn't have to keep the second one a secret from the first.