This topic is quite interesting.

I will agree with Topper that on most Broadway-shows that are now touring, they will replace a lead or supporting actor instead of hiring local talent or using the "understudy."  Generally, if it is a large-enough name (such as Robert Guillome when he took over from Michael Crawford in Phantom) lead and the director is available, he will rehearse the actor with the company.  Sometimes the replacement actor will demand the director's presence. 

Otherwise, the stage manager ends up directing the actor and company--one of those other reasons stage managers should keep track of all directing/other notes given to actors so they can keep the show truly to what the director intended.

The cities--most of the tours I've seen have a plot like this:

1st year on tour:  large cities music centers and theatres:  downtown Chicago, downtown San Francisco, downtown Los Angeles, downtown Washington D.C., etc.

2nd year on tour:  the suburbs of large areas (you still need a large enough area to sell enough seats):  Oakland, San Jose, Santa Rosa (Bay Area); Thousand Oaks, Pasadena, Orange County PACs (LA), San Diego, Santa Barbara, Nashville, Phoenix  (smaller areas, but still enough for ticket sales). 

Of course, the producers will look at how a show "did" on the 1st round of the tour.  If ticket sales were off in a particular region of a country, they probably won't return to the same region the second year  (i.e., a right-wing pro-military piece in Northern California or Oregon or an amoral play with vulgarity and sensuality in the Bible Belt).

As for the route, you could use the inconvenience of travelling half-way across the country every other week as part of the conflict building in the company.  Everyone--no matter who they are--gets tired of living out of a suitcase and hotel room after 6 months, especially if they are with the same roommates all the time.

Every tour is slightly different, depending on who's sponsoring it and so on.  I can only speak generally, from my own experiences.

1) Trucks are still the most efficient way of transporting sets, lights, etc.  Even if they were shipped by train or plane, you'd still need a truck to get them from the depot to the theater.  Every professional theater has a loading dock for this purpose.

2) "... stringent system of checks" ?!  I nearly choked on my coffee when I read that.  True, a quality stage manager and company manager will typically have everything under control.  Even so, the best laid plans ...  While it is rare to have an "whole costume rack" go missing (the wardrobe person would easily be fired on the spot), it is not unusual that a mislaid prop, set piece or costume does not find its way onto the truck.  If it happens repeatedly, the person responsible can be cited or fined by the producer, so everybody is pretty reliable about such things. 

If the item was important enough, it would be up to the CM (and/or SM) to decide how to replace it.  Having the previous theater ship it is one option (if there's time), another option would be to replace the item by purchase or rental (hence the fines -- the producer has to make up his money somewhere).

What would be more likely is if the prop truck or scenery truck was misdirected, broken down or involved in an accident.  This would delay the load-in considerably and give you the dramatic situation you're seeking.

3.  Actors are SUPPOSED to check their props, yes.  Do they always?  Hah!  It only takes once for a prop to go missing before the actor decides to check them every time.

4.  In professional theater, warm-ups are typically left up to the individual performer.  It is part of their job and, as such, if they strain or injure themselves due to improper (or non-existent) warm-ups, they are effectively putting themselves out of work.  It is not unusual to stroll down the hallway where the dressing rooms are and hear a cacophony of moos, trills, and la-las emanating from within.

Sometimes the dance captain might call a quick run-through of a number if the SM noted something sloppy in a previous performance.  If there's choreographed violence, then a fight call is always scheduled before the house opens.

5.  There is always tech!  Hopefully, for the performers it is a "dry tech" where the performers are not called and the SM simply runs though all the cues with the stage crew to make sure everything is in place and working properly.  However, every theater is different, so placing sets props and other things in the off-stage spaces changes from place to place.  It is beneficial for everybody if a tech takes place.  Sometimes it is constrained due to time issues (like the truck was late)!  Nobody can avoid tech.

"The performers have a turbulent flight..."

I didn't catch this first time through, but I don't believe this would be accurate in the scenario you're trying to create.  It is extraordinarily rare for a Producer to fly his entire cast anywhere.  Unless your producer has his own private aircraft, it is simply too expensive and not a cost-effective way to transport a large group of people. 

Broadway producers are polar opposite of Hollywood producers (even to the point of being on different coasts.)  Hollywood's answer to solving problems is throw money at it until it works (and since it's being captured on film, it only needs to work ONCE.)  Broadway's answer is to find a cheaper way of doing it or cutting it out altogether (Hey, we're doing this show eight times a week!  Do we really need all those Cats?).

Most performers are trucked together on a bus or "motor coach." (Call it what you will, it's still a #%$@! bus).  The reasons are many:  Namely, first and foremost, cost!  A bus can be rented by the week; plane tickets need to be purchased at every stop.  The coaches vary wildly in quality and comfort -- some may have sleepers, some may have a lavatory -- most likely, there'll just be large seats that recline somewhat with scheduled potty breaks or stops for food.

Another reason is that the motor coach keeps the actors, crew and their luggage all together in one spot.  The CM or SM has one less hassle trying to round up everybody.  No wasted time waiting around terminals for baggage to be checked or cleared.  Nobody is rushing to catch a plane and nobody gets left behind at the snack counter or restroom.  It's the same mentality that goes toward herding cattle:  keep the group together at all times.

Some larger tours may have designated "smoking" and "no smoking" buses but this is rare.  Most tour buses are "no smoking" and there are always several performers (or crew) who opt to drive their own vehicles in a caravan following the tour.  This gives them the option to smoke the entire trip, and it also allows them to have a car in a strange city and not rely on taxis or public transportation to scope out the night life after the show. 

Those who drive are sometimes paid a stipend for gas (which is never enough).  Parking, tolls, tires and general wear & tear are their own responsibilty that can be written off on their taxes.

In the case of the understudy replacement that you mentioned in previous posts, it would be understandable for the producer to spring for a plane ticket in order to get the new actor into rehearsal ASAP.  If there is no rush, the producer would just a soon offer train fare or a bus ride.

I've even heard of Producers tell their freshly-auditioned cast:  "Our rehearsals start on (Date) in (City).  Call the CM's cell phone when you get there to check in and find out where you'll be staying."  (The guy wouldn't even pay for transportation to get the cast all in one place to begin with!)

Hope this helps.