You never know how its going to work out, but yes, you need to do immigration (and baggage if appropriate) at your first point of entry to the US. In my experience, baggage doesn't make much difference. There is usually a baggage re-drop facility immediately after clearing customs.

Our experiences at PHL and LAX were very quick, probably less than 30 minutes, and we ended up waiting when we could have been on an earlier connection. Of course, had we planned that, we would have either missed it or at least been somewhat concerned - you cant win. Arriving at MIA (fortunately not connecting) it took almost 2 hours to get through, so now we try to leave ample time or stay overnight at the entry point. We had conditional approval for GE but that got timed out by Covid.

All that said, if you are wanting to maximise Tier Points, you might want to look at splitting the LHR-LAX leg into 2 eg LHR-JFK-LAX - which would get you an extra 140 TPs each way - and would probably change all of the connection times too.