OP should be a little bit more optimistic, assuming that OP could find a different date with the identical route and longer layover. I changed my Basic Economy ticket from late January to early January, 2020 because the original/changed connection time was illegal (below the minimum). An agent was happy to change the date for me. I did not need to use HUCA.
Good luck.

Flying UA 1762 LAS-LAX, connecting to NH 5 LAX-NRT on one ticket in March in Y (well, K actually). Original scheduled time for UA 1762 was 08:15 (LAS) - 09:16 (LAX), now changed to 06:00 (LAS) - 07:01 (LAX).

Used my miles for friends to fly in F on the same NH 5 flight, so my re-booking options must include this flight - other options, like a later departure from LAS via SFO won't work for me. This makes me rather inflexible, so this time change has hurt me more than any other in the past.

(I have also booked a separate one-way ticket for my friends with my miles on the same LAS-LAS UA flight, but I can easily just cancel that based on the time change.)

I get off work here in Las Vegas at 4:30 am and will not be able to make it to the airport on time for baggage drop off; after the 6 am departure, the next one is 10:35, arriving in LAX at 11:44, not leaving me time to make the NH 5 flight at 12:25. (I won't be able to get out of work early or get an extra day off either - I'm locked into leaving work at 4:30.)

Essentially I need to make my LAS-LAX a non-UA flight.

I've looked at the pricing for a LAX-NRT, NRT-LAS flight, but that's about $200 more than what I've already paid.

Can I either....
(a) Ask UA to just drop the first LAS-LAX flight, and I'll buy a $49 ticket on Southwest and make my own way there? (And possibly get a partial refund for that portion of the ticket? Not the biggest deal, but it would be nice.) Obviously I can't just skip the first flight; I know that will cancel the whole ticket.
(b) Wait as long as I want, in between now and March, and if the price for the new LAX-NRT, NRT-LAS ticket drops to less than what I've paid, cancel what I currently have based on the schedule change? (Is there a time limit for requesting a cancelation based on the schedule change?)

I'm platinum this year and in 2020 (and was lined up to make it for 2021 already until the changes - now I'll hit silver at best...)

Thank you for your help and advice!

Yes.

Yes (no limit).

UA understands that most people don’t check their reservations obsessively. If pushed on it (you won’t be), just say that you’d thought you’d be able to get someone to cover your shift, and it turned out to be impossible.

LASNRT : I would call the Premier Line and, explaining your predicament, ask if you can drop the LAS-LAX flight (and I think they probably will) BUT ask if they will put in comments authorizing you to re-instate the LAS-LAX flight at a later date if another schedule change (quite possible between now and March) makes things work again. That latter part would probably be a hard-sell. But, be ready to HUCA if the agent balks at either request.

OR, you can just leave your booking as is, book a separate refundable ticket on another airline, and wait to see if the UA schedule changes back to something usable.

Thank you both jsloan and 1984SW for great advice! I've never been this locked into a particular flight before, so I appreciate the opinions!!!

I think for the moment, since there's no time limit, I'm going to leave it as is. I think it leaves me with the most options. It's still 5 months out, so I'll see if any other schedule changes develop in the next couple of months. If things don't change to my advantage I'll ask them to drop the LAS-LAX portion.

Thank you again!!!

What was the response when you called back a second and thrid time?

Oops. I waited too long to call and now have a third schedule change and the 'too short' layover no longer is.
It seems all things work out in the end.

Haven't called back again. It isn't showing as a schedule change any more on the website so when I am in the UC next I am going to ask one of the agents in there and try my luck that way.

Would a change of departure time by 1hr 15min (earlier) normally be sufficient grounds for a refund?
This change makes my separate ticket connection difficult (and there are no alternative ua flights that work for me unless I wait a day)

Officially, probably not, though you may have luck if you find an understanding agent and explain to them that the change simply doesn't work for you.

Called cs, the first agent sounded annoyed and unfriendly. Not to tempt fate, while she put me on hold, I used the opportunity to get off the line. Second agent was pleasant, cxl and refund without issue. FWIW.

What's your point?

I went from having nearly zero leverage to having truly zero leverage.

Nothing changed with regard to the amount of leverage that you have unless the flight times went back to exactly what they were before. The fact that a schedule change is no longer highlighted is meaningless.

I personally find RNE's advice (in the signature) to be too aggressive and slightly distasteful, but if you thought that it was worth calling before, the situation doesn't seem to have changed.

I agree with your opinion of RNE. That said, distastefulness is a matter of degree. Up to three calls is palatable and worth the effort, methinks.