40 ma is not that serious, and assuming it's a more or less accurate figure (within the tolerance of your VOM), I'd say that there's another issue at work. Consider that the glove box or dome light bulb (if you left the door open) will drain more than this, and your battery if healthy should easily tolerate this overnight.

I'm thinking that your battery is toast. You mentioned that you just rehab'd your alternator -- I think that the history of your battery suffering from poor charging prior to that repair might have caused irreparable damage, so that now it just can't hold a charge for long (i.e., overnight). Remember that I wrote earlier that a battery left below 50% for long periods will become sulfated -- I'm thinking that this happened.

You can try to have it charged properly using a multi-phase charging regimen, but I don't think it will restore the battery.

In addition to my suggestions (e.g., checking the individual cells for specific gravity) and someone else's, too (e.g., a load test), I think you'll discover that the battery just isn't up to the task anymore.