Hello and welcome to the RTA forums !

It would seem you have just made note of the two routes suggested by Google which are not your only choices, for example you could go St Louis, Denver, SLC in a similar amount of time. Even going via Dallas and Albuquerque up to SLC would only add 2 or 3 hours over the 6 days, but I'm not sure I would be looking to add time. You really won't have time for any major sight seeing, just regular rest breaks on the drive and a little time spent where you end up for the night, so it comes down to whether you prefer one over another for what ever reason. The most important thing is to treat the journey as a marathon and not a sprint and break your journey into equal segments. The temptation is to push too hard on the first two or 3 days when you are fresh and then quickly become fatigued after that which can lead to misery. Also keep in mind that when you are capable of keeping to the speed limit you will only average around 57mph over the course of a day by the time you have taken rest and bathroom breaks, filled with gas and eaten etc so if you are restricted to 55mph you will be lucky to avverage 48-50 mph each day. Taking 'slower' roads because you cant go fast will also eat into your average time, bends, hills and towns will be taken slower and decreasing and increasing speed takes longer. One tip to save some time would be to stay out the 'other' side of town as you head north and west so that as the morning rush is heading into town, you are heading in the opposite direction and will avoid the worst of the congestion.