I am not sure you understood my instructions.
You use the older 12.6.5 version of iTunes so you can download the CURRENT version of the app into iTunes.
Then, go back to your older iPad and in the iOS App Store under Purchases, you look for the DropBox app.
Then, try tapping the download “cloud” icon next to the DropBox app, in this location, to see if the small window pop-up prompt that states that there is an older version of the app that is compatible with your device. Would you like to download this version now?
Tap the OK button just below the prompt to start the downloading of the older app version to your iPad.
Is this what you did?
You are NOT going to get an older version of the app using an older version of iTunes on the computer.
You download the most current version of any app to the older iTunes 12.6.5 version, then attempt to get the older version of the app on your older iDevice after downloading the current version of the app into iTunes 12.6.5.
Is this what you did?
For any older app versions, that may still exist in the iOS App Store, this is THE iTunes procedure that will work every time to obtain older versions of apps for your older iPad. Not just to get a single app.