Respectfully, you couldn't have done your current measurement correct because it can't be 0.00. There needs to be current at the very least for the computer & theres various bias resistors as well, so you should see at least 20-30 ma. I cant remember the exact draw as I did an electrical problem once but its what I said or more, I have a 2003 Impala 3800. Any multi-meter requires you to put the Red probe in a different post than that for making voltage measurements, additionally you may have one for mill amps and one for greater than 5 or 10 amps, look at your meter and make sure the probe is pushed all the way in to the meter. Just opening your car door will wake up the computer, putting the key in the ignotion without turning will wake up the computer, Ky In and in Asscy,On, Start all activate different relays or the computer engages different electronics and each position will have a different current reading. Plus the current will jump all over, up and down in any of the other conditions. I hooked my meter up and just opened the car door and could see the current going up and down, same with turning key to asscy or on and after pulling the key or shutting the door, I could see the current changing for about the next 4 mins, until the computer went to mostly sleep mode, but you should see something in the 10's of milliamps.
Dont pull every fuse one by one as that video is showing. Under the hood there are 2 fuse boxes on the passenger side, open the covers, you will see 4 60 amp fuses in the top bog and 4 in the lower one. Pull each of those one by one. Everything goes thru those except the starter, crank relay, generator and ECBM module, unless you have a Police car the battery will also got to 2 SEO circuit breakers. But those 4 loads do have :fusible links", which you can look at as a fuse in the cable leading to them and they are not something easily poped in and out. Otherwise the battery feeds those 8 60 amp fuses and all other fuses and relays are thru those 8 60 amp fuses. The only way you read 0,00 amps is if you popped one of those fuses.
So I assume when you have this power draw its when its sitting overnight no key in?
When you said "It initially started with the engine having a random delay in trying to start. Sometimes it would fire right away, other times it would be a 2-3 count before anything would happen. That 2-3 count turned in to a 10-15 count which then progressed to no crank at all", you mean the crank was actually turning as normal, normal sound normal strength but no engine start.
What did you mean by "delay". You turn the key and there is no crank turning, not crank sound, nothing at all, then all of a sudden the crank turns?
When you talk about the time progressing, is that all the same time you are trying to start the car at that time or did you mean one day is was 2-3, the next day it was longer, the day after even longer, next day nothing.?
So try pulling all the 60 amp fuses and see if battery dies over night, if so, you know it thru one of those, you can then check with a current reading by pulling each, but like I said, you have to wait for 4-5 minutes for your computer to go back to sleep and then see if there is excessive current flow. If you pull them all and your battery still dies, try isolation the generator, its easy to disconnect the main power cable to it and pull the control cable, even though thats off the fuses, something could still be wrong there. There are regulating diodes in the generator that is usually the failure method of the generators, so try that. You can pull the crank relay, perhaps its stuck or has a path to ground or a problem with the signal the computer drives to enable it. The starter is a bit more trouble, you can disconnect its power feed as I recall on my 2003, either the generator or the ECBM module's cable is wired to the same post on the starter, so by removing the battery to starter cable on the starter post you also remove batter power from the gen or ECBM, its just a convenient place tp route the cable from, nothing more. You'll need to remove your bottom plastic cover under the front bumper to get at the starter, its possible its bleeding current somehow. The ECBM is somewhat a pain to isolate, I remember doing this. I dont fully recall, but its a real pain getting the power cable off of it, either due to access or the mechanism itself is not obvious., but it is not very at all likely thats the problems. Try the 8 60 amp fuses firts, then if still failing try isolation each of the other hardwired loads like I said.
The other thing you can do is visual observation. Look at all the cables in the engine bay on its top, bottom and side. You are looking to see if a cable is rubbing on or pressed against something. This is how cable shorts occur over 50-1-- miles, just gentle rubbing, all that adds up.
You did get a new battery, correct? Hope this helps, if you can verify the power issue as a power draw I can help.