Josiah's notebook gives you the carriage lock puzzle AND the trivet puzzle. It's a long puzzle.
There's also a clue about the trivet, in Jim Archer's typewriter. I'll have to test that. Do you need the typewriter or the notebook to start the trivet puzzle. Do you need both? If I only need one of those clues, then I'll skip getting the other one.
The trivet puzzle is long. What you do is go to Twin Elms, then to Titusville Telco, then to the orphanage, then to the printer, then to the fishing hole, then to the printer, then to Titusville Telco, then to Twin Elms.
Maybe you could split the puzzle in half, as a timesaver. Titusville Telco is the spot that's closest to the Lilac Inn. So one of the trips there can turn into "visit Titusville Telco, go back to Lilac Inn and do stuff there, finish trivet puzzle the next time you go to town". That's not the worst idea ever, since you have to visit Jim Archer two more times, before you get the second half of the trivet, at which point, you DO have to finish the trivet puzzle.
So...I guess I can chart out routes, time them, and determine what's fastest.
What happens if you run out of gas? Does the game automatically send you to the gas station? If so, maybe you could plan things so you run out of gas at a certain location, then get warped to the gas station. That could save time! Obviously, it'd save time if you never have to get gas.