It's probably a huge difficulty but the obvious solution is to hire more officials so that they don't have to travel as much. Also it seems like it should be possible to schedule the officials games within a relatively short distance, especially since the officials are not limited to one conference. For example, a crew could be at a Baylor game on Saturday, a Texas game on Monday, an Aggie game on Wednesday, & a Houston game on the next Saturday. TCU, SMU, plus all the G5's in the state provide lots of opportunities. For most regions in the country it's similar ( the Florida & Georgia schools in SEC & ACC; the P5 schools in the Carolina's, Virginia, Maryland, & Pennsylvania, etc).
Finally, if the problems with Big 12 officiating (& likely other conferences too) is due to fatigue, quite possible, then the conferences or NCAA should limit the number of games an official could work in a given week or establish similar controls until the regional arrangements above can be implemented. Since the reason some will work so many games is likely the desire for more money, and to attract more & better quality officials, they should be paid more. Incentives matter.
It's a complicated issue and potentially a huge issue. The ejection of three Big 12 HCs in 9 days helped bring it to light but it doesn't get much attention. The TV announcers often go out if their way to claim that they are great officials even it's doubtful. It's propaganda that they are probably told to spew out. We never know how bad it is because the people who in the know are tight lipped.
I can see opportunities for some clever entrepreneur: establish a company (especially football & basketball) to train, hire, & schedule regional officials in the various sports and sign contracts with the conferences to provide them. There would be lots of details to work out but it could be a win win situation for everyone.