If it were me, I'd start by putting my D&D books aside and then go looking for sourcebooks from other games that are of the era that you speak of. Like I wouldn't be surprised if there was a GURPS sourcebook for Industrial-era, Victorian, or WWI-era gaming. So I'd pick up one of those... find out what the sourcebook indicates are the most important historical bits and bobs that the designers of that book felt they needed to build mechanics around... and then go back and mix and match 5E mechanics to reach a similar place (if indeed running the game using 5E matters that much.)
Because I just think that if you start at 5E and merely try to push the game forward in time-- adjusting classes, races, equipment, combat rules and so forth as you go to try and make them "Industrial-like"-- you are going to end up with a game that pretty much is exactly the same other than a couple mechanical changes here and there. And thus not even hit upon a large amount of the actual setting material you'd probably want. In other words... pushing the Cleric or Wizard forward as a class into the Industrial / turn of the 20th century era does nothing but muddle the types of character classes you should have for classes of that era.
Make a full break of 5E staples from the beginning, create the setting and game from the time period you want to begin with... and then see if anything after that from standard 5E could be incorporated just as nod to the original game.