So how do I get an image from develop to the filmstrip?
If the image is visible in the Develop screen- simply click on the top menu [Print]. The image will remain selected on the filmstrip ready for you to drag to the Custom page layout.
(Function key 6 [F6] toggles the filmstrip visible/hidden)
The FIlmstrip contains photos depending on the mode you are viewing, be that ALL Photographs, a selected Folder of images, A Collection of images
To limit the photos on the Filmstrip- I suggest you place photos you want to print on the Custom page into a Collection (Quick or Standard) and select that collection before Developing selected photos and printing.
My example is that I have the [All Photographs] list active so I see all my photos on the filmstrip- going to the Print menu from Develop keeps the one selected image visible on the filmstrip.

Regards. My System: Windows-11, Lightroom-Classic 15.6, Photoshop 27.8, ACR 18.7, Lightroom 9.4, Lr-iOS 10.4.0, Bridge 16.0.3 .