The custom forms should copy into the new .axf. When you check out, click the checkbox to pick a form. Place a copy of your current .axf somewhere for reference and choose that .axf to copy your new forms in that image. When your done, save the map and every time, you will be able to use that map w/o navigating back to that .axf as long as you keep the original .axf that the copies will be made from.
All the forms will copy, but if you need to include DBf's, they will not copy, but if you need dbf's, what you can do is keep the same folder (ex DataForArcPad1) in ArcPad. Use the same map and everything and just switch out the .axf file and nothing else. All the dbf's will be in the appropriate places if they are needed.