Another option for you would be a baggage delivery service, for the bag that doesn't have the firearm in it. Put the gun in the wheeled case and take care of it yourself. Let the baggage delivery service handle the non-wheeled case. It will be delivered to your hotel and you can have a bell person bring it to your room.

I used Bags VIP a few months ago on a trip to NYC. I checked a bag and didn't want to hassle with it on the subway. I did hang around in the baggage claim area until I saw the courier pick up the bag. The charge was about $29 and worth it to me. I'm sure there are more delivery services in LAS, but Bags VIP has been in business for several years and they do a lot of business in LAS.