And,in this case, I'm the caveman.
Some months ago, I got introduced to an online app that allows you to practice your skills with redistricting. I gave it a try, and was impressed. I made my own 4-district map, which took a couple of hours. Using current population estimates, and only being able to draw lines along current voting precincts (something the actual line drawers don't have to do), here is my vision for the four districts:
District 1 (blue): 684,557 residents. Box Elder, Cache, Rich, Weber, and Morgan Counties, plus all of Davis County except North Salt Lake.
District 2 (green): 684,358 residents. All of Southern and Eastern Utah (including Wasatch County), Summit County except Park City/Kimball Junction, and Utah County from Provo South
District 3 (purple): 683,873 residents. Tooele County; Utah County from Orem North (including cities west of Utah Lake); and Salt Lake County cities Draper, Bluffdale, Herriman, Riverton, South Jordan, West Jordan, Sandy, Midvale, Cottonwood Heights, Alta, and surrounding unincorporated ares.
District 4 (red): Salt Lake County cities of Holladay, Murray, Taylorsville, West Valley, and Salt Lake City, with surrounding unincorporated ares; North Salt Lake in Davis County; Park City in Summit County.