I have experience with shipping gear from working at a rental house, though I haven't shipped my Steadicam gear for a job yet (only flown with it).
Generally shipping companies won't insure for very high values as they want the customer to have their own insurance. In the rental house world, gear is typically insured by the end user, though in some instances the rental house ends up insuring for transit. In these instances, some rental houses choose to take the UPS/FedEx/etc. insurance and insure for their deductible. For example, if your WP Dolle policy has a $500 deductible, you would insure the shipment via FedEx for $500, and the rest would be covered under your WP Dolle insurance.
If you're able to have production's insurance agent write into the COI that your gear is covered in transit, that is ideal (can be spelled out under description of operations). If the shipment isn't related to a production, then I would insure under FedEx or whatever shipper you use for your WP Dolle deductible and your WP Dolle insurance will cover the rest in the unfortunate event anything happens.