I don’t have an iPad, and I’ve not had to transfer large files such as videos between iOS devices so I’m not the best to ask about this but I am aware of a few options.
As I understand it, the only way to get the original video from the phone to the iPad is via iCloud...[and not to remain on the iPhone]
Not the only way by a long shot. I investigated two methods of moving videos from one iOS device to another iOS device, in my case two iPhones.
You will need to have iCloud Photos OFF for your iPhone, otherwise the videos you shoot with the camera will save to Photos and upload to iCloud Photos
1 - AirDrop
You could use AirDrop to copy the video files from your iPhone to your iPad. This would deposit them in the iPad's Photos app, and from there you could save it to the Files app on your iPad. Both of these actions have implications for iCloud syncing - if it’s activated on a device it will upload to iCloud because both Photos and iCloud Drive (ie. Files app) are syncing locations. This is what happened when I AirDropped a video from my secondary iPhone (not on iCloud) to my main iPhone (on iCloud).
The only catch here is that if your video files are chunky space-hogging monsters then it may take a while to copy. I am unaware of any size limit for AirDrop.
How to use AirDrop on your iPhone, iPad or iPod touch
How to use AirDrop on your iPhone, iPad or iPod touch – Apple Support (UK)
Use AirDrop on iPhone to send items to nearby devices – Apple Support (UK)
Use the Files app on your iPhone, iPad or iPod touch – Apple Support (UK)
2 - Copy your videos from your iPhone to your Mac, and then from your Mac to your iPad.
iPhone to Mac.
You can copy the videos the old way by importing them from your iPhone by using Image Capture. This application will drop them in a folder or desktop. Image Capture is more like a Mac's Finder than Photos; it is a file manager for image files and was used mostly to get photos from a camera to a Mac. At the import stage you can remove the videos from your iPhone as you have indicated that you don’t want to keep them on your phone.
See: Transfer images in Image Capture on Mac – Apple Support (UK)
Once they are on your Mac import them into the TV app (TV app Menu Bar > File > Import) ready for syncing to your iPad.
Mac to iPad
The next step is to get the video files onto your iPad by using a cable to connect and sync it from your Mac over to your iPad; when you choose the option in the Finder sync it is imported it into the Home Movies collection in the TV app - which now manages videos as iTunes once did. It’s my understanding that the TV app does not sync with iCloud, even the Home Movies collection so this does not affect any choice you may want to make about your iPad participating in iCloud syncing.
This does though require you to keep the videos in TV app on your Mac. If you whip it off your Mac the next time you sync they will be deleted from your iPad's TV app, however if you copy a video to Files the TV app copy is expendable. The iPad, and indeed iPod, were designed as satellite devices not as stand-alone devices and depended on a computer to house the content. You would know more than I about the iPad, so perhaps this has changed?
Anyway, I tested this on my kit and this is how it worked.
And again, back up your videos; don't rely on having them just on your iPad.