If the pump has a nice finish, bring several large moving blankets ($5 each at Harbor Freight) and wrap the pump with several layers of blankets, then secure the blankets with an industrial roll of Saran Wrap or duct tape. Then use the board method or just slide it in. If you use enough blankets, it won’t hurt it. Trust me, I’ve moved a few.
You can see the pump I restored, wrapped on this trailer with several blankets (a pink blanket on the outside).