Thread title says this is "not because of Delta," except that it is because of Delta. But at any rate, OP seems to be faced with one of the uncomfortable dilemmas in travel: when you see possible connection problems developing, should you try to fix them in advance or work them out as you travel along?

Flying in from abroad it gets trickier. It sounds like the OP's calls, together with status, eventually triggered DL to implement some high level fixes to get him home. But then the original schedule became workable again. In short, it is now a mess of good intentions by all.

Some of the earlier advice in this thread is often best -- go to the airport for the original flight ready for travel, and let Delta handle the situation as it goes from there. Getting to a ticket counter, and eventually to ticket or gate agents in LAX, and letting them accommodate you and your luggage situation is usually best. Remember you have status to try to avoid lines and you have a SkyClub in LAX, usually with 3-4 extra-helpful agents on duty.

I usually don't try rebooking unless I already see (for myself) a very clear path to a solution.