I'm not sure I get your question. How are you getting to Nevada from SLC?
Are you transferring planes?
If not, why don't you eat when you get off of the plane and then get your bags and wait for your people? Most of the restaurants in airports will pack your food to go. Put it in a box, go down and get your bags, and find a place to sit outside of security, eat, and relax. Even if you are a little late, the most that will happen is that the airline will take them and put them in their office area or in a designated spot. You just have to ask if they are not still on the carousel.
As far as the liquids; if I am going on a weeks' trip, I pack everything and send most stuff in my luggage, but bring a few sample sizes in a carry on bag. There are plenty of contact lens solutions in 3 oz. sizes or less and you probably are not going somewhere where you don't have access to a CVS. I always have 2 ziplocks with stuff, some make up, some contact like stuff and I have never had an issue. I bring a lot of stuff when I travel, since it usually involves some kind of exercise clothes, as well as regular stuff. The only time I brought carry on luggage is when I went to AZ for my in laws funerals.. 3 day/2 night trips. I get mighty annoyed at people who try bringing heavy and large carry ons because they are too cheap to pay the baggage fee. The departure gets delayed when the airline personnel are asking people to check these bags and there's often no room for coats or my one little large purse/carry all in the overhead bin.