After a hideous amount of time and effort, I finally found a way to get my apps that are "no longer available on the App Store" and do not show up under "Purchased" from my old iPad to my new iPad Pro.
It requires that you have backed up your computer over the past few years, or at least one year.
Ensure that your iPad is not plugged into iTunes. Close itunes.
Find your backup.
In Finder, search ".ipa". (Note: just searching for the app name.ipa does not always work, nor will searching for the iTunes mobile applications folder always display the .ipa files within it. No idea why.)
Locate the .ipa file for your missing app or apps.
Copy them to a new and accessible folder.
Open iTunes. Click Library.
"Drag and drop" your .ipa file INTO the field of app icons. They should copy over.
Now plug iPad in to your computer.
Click on the little device icon to open up your device in iTunes.
The list should now include your missing app.
Either drag it onto your Homescreen on the righthand panel, or change the app's button to "Will Install".
Dialog appears: "You've changed settings... apply?" Click APPLY.
Apps should now be installed on your device!
If only a few of your apps install, and you get an "Could not sync xx number of apps" error, disconnect and do a hard reboot of your device (hold both buttons down), restart and reconnect. Check in iTunes that things have not been reordered; reposition if necessary, then click DONE-APPLY again.
Related things I have discovered, to my dismay:
Apple is culling older apps off the App Store at an alarming rate - three times as many last month than ever before. Back up your apps now, separately!
Itunes no longer saves your full app, so it is up to you to do so manually.
In Setting-About on the iPad, a list shows on the left supposedly of all the apps installed on your device. THIS IS NOT ACCURATE. I did a spotlight search and found dozens of other apps that were actually installed, but not showing in that list! Some of them had icons on the screens, too.
Further, when I did a restore from the older iPad to the newer one, the newer iPad not only did not list every app that ended up installed, but some apps that did NOT SHOW IN THE LIST AS INSTALLED on the old iPad DID install on the new one, verified by Spotlight search! The moral: do NOT rely on that list!
Some older apps that started with a symbol of digit have been renamed with it spelled out. Adjust your search to that. Example: #photos is now Hashphotos.
Some older apps were discarded and started anew by the developer, with a similar but not identical name. Find the name of the developer for your app and search as to what other apps they have made. You may find the newer version, and if it requires payment, sometimes contacting the developer and telling them you have the old one that won't work now will result in them sending you access.
Some older apps do things that Apple is not allowing anymore. In some cases, by installing the oldest .ipa version you can find in your backups restores its original functions... if you are lucky.
If you do manage to install some very old apps on your new device, they may not work well, or may just plain crash. No guarantees.
No app icon showing up on the device, yet Spotlight Search finds it? You may have all your Homescreens filled up to capacity. There is a limit (20 pages, I believe; do not quote me on that). If this is the case, apps WILL install, but the icons themselves are "hidden". Once you group apps into folders and free up spots for icons, they will one by one appear.
I hope this helps someone, and you do not have to go through what I did to learn all of this from scratch!