The big wildcard is the weather. At this time of year we always plan on ending up on I-10 and coming up to PHX from the south. Then the only question is how far south how quickly?
Re the route you mentioned, 54 from Santa Rosa is a good road. No real hills. It's sparse, but there is gas every 35 miles or so. In good weather, you could then turn west onto US 60 at Vaughn NM, and take that all the way to Apache Jct. It's scenic and it's a good road, BUT it does have some fairly strong hills and some hairpins as you drop down to and up from the Salt River. I have never tried it in mid-winter. I think at the higher elevations you should expect snow.
Or instead of taking 60, you can stay on 54 down to Alamogordo, then take 70 to Las Cruces, then I-10 west. There are no real hills to challenge you there. But it can still snow. Roswell had 18" of snow last week. It's not common but it happens.
If the weather allows, and we watch it closely, we will go through Tulsa, OKC, & Amarillo, then down through NM as above. But most years we allow for going through Dallas or even bypassing it to the south, to be in better weather. That basically adds a day to the trip. But if weather permits, we will do the OKC route instead. In your case you'd probably be looking to go through KS if you get good weather.
So bottom line, plan two routes. One that's pretty direct, and one that will give you the best shot at avoiding snow storms.