I constructed the order of speedrunning Mario is Missing based on a world recorded attempt by Iceplug. This route only works for the Super Nintendo as the MS-DOS, macOS, and NES releases are different. At some point, I will write about how the RNG works as I attempted to come up with a "bulletproof" method to complete this game but have since shelved the project due to other priorities.
The order is as follows:
Deviating from the above order will cause the position of items to change from the map I have provided. Additionally, the use of passwords will also change the item placement, so this is built on the expectation that you'll complete the game in a single setting. You should be able to finish the game in under 30 minutes if you follow the above order.
To efficiently complete each city, making use of the pipes is the most effective way. You can use what is available below to determine where the pipes go. Since the items are moving the moment you enter a level, it is worth spending time determining where they'll be so you can time pipe use appropriately.