Perhaps I misunderstood, but is a continuous signal from the DVDs
practical? Is the show timing such that everything else can match to the DVDs? It would seem to be potentially awkward during rehearsals or if something happened during a show.
Speaking of which, if you have to stop or pause the DVD players, will they stay in pause indefinitely or do they stop after a short time, causing you to recue them all? How would you cue and control the DVD players? This may be planning for "what ifs" but it is one area where a real matrix router would be beneficial as you could have one local monitor that could be fed from any DVD player for cueing and monitoring.
You also did not mention how you are addressing audio related to the DVD sources, are the three switchers handling that or are you running each DVD output directly to the mixer? With the DVDs continuously running the latter approach might mean muting different DVDs at different times (you don't want three sources of the same audio active) or maybe putting all the related audio on one disc.