Do your prices include gas? Because in my calculations that was an extra $1k on the trucks...and would probably trash a car's MPG, especially if you were pushing its capabilities.
When my bf and I moved from IL to SoCal (LA area) 1.5 years ago, we found the best (cheapest/least hassle/least risk) way to move was to put our stuff in a UHaul U-Box (~$1k for 1 5'x8'x?? crate) and fly, then buy a car on this end. The tradeoffs would have been different if we'd had a car already though (my colleague did the roadtrip...but also sent stuff via U-Box). We also had no pets. You can also look into shipping stuff by Amtrak; I think you have to call or go to a train station and ask, they don't have a lot of info online, but it can be economical for smaller loads (it was our backup plan in case we had a few large boxes left or something).
If you don't like/trust UHaul or their boxes there are other services where you pack and they deliver, either into a pod/crate or into a truck (PODS, U-pack, etc...we had a good friend recommendation for DoorToDoor but they didn't work for us geographically, they do operate in Chicago though!) I would give the pod/crate/box form of moving a 4.5/5 for price and convenience. I would give our Uhaul experience specifically more like 3/5: the franchise at our origin was awful, I wished they had a tracking system, but the experience/service on the LA end was great and redeemed them. Basically, shop around and read reviews, but if UBox is tantalizingly cheap, you can go with them and MOST likely be fine (take valuables with you...), just give yourself buffer time if possible in case your case is mishandled.
Even if you have to buy or rent a car in Chicago to get yourselves and the dogs to SF, you would get rid of the towing requirement and could go with something more compact (maybe even cheaper?) without risking being unable to make it up the Rockies!