Get into the routine of entering them as soon as bills come in or putting the bills in one location, entering them once a month and writing on them that they were entered/paid, then filing them. 

If you feel uncomfortable with that $850k price tag, I would pause and recommend attending RE meetups in your area and getting feedback from other local experienced investors on San Gabriel Valley and other parts of LA.

This still makes me uncomfortable because the apartment will have stuff from Tenant B inside before Tenant B's lease starts, but with Tenant A's lease going until the end of the month (and them having paid for it), I'm not sure what to do about it.

This is where a GC can really screw you.The GC/Investor relationship is a murky, volatile, uncomfortable swamp with many nasty creatures lurking. 

I've worked in insurance for over 20 years and I've never see it be this hard to get routine coverages.

The gurus never tell you that searching through the smoke and the mirrors in the game, extending yourself very uncomfortably into the unknown, being willing to invest and possibly waste your time searching for answers, actually building meaningful relationships, all of that's is a very big part, if not the biggest part, of winning in real estate.When Hannibal was told it was impossible to get his elephants over the Alps to invade Roman territory from the north, he responded with the following:"Aut inveniam viam aut faciam" I WILL FIND A WAY OR MAKE ONE.That's the attitude we need here.

You will do better door knocking when you feel comfortable, and when you feel comfortable the people in front of you will feel more comfortable and they can tell (but we should also not feel like you are dressing for your living room either), and so dress how you would want to dress, in a way that is clean, professional, but more casual in clothes that fit well and are not uncomfortable to tight or too big--  otherwise you will feel it as soon as you knock on the door.  

Which of the two options make you more uncomfortable?

After enough time in this business, most especially in C-class, you will worry routinely that you're not throwing your plumber or your HVAC guy enough work.8.

Maybe you can Network at least once a week. put in one offer a week.I'll add that to the routine.