There is no difference between a drop ship and a regular shipment.
You do the PO, receive the inventory in PO, invoice in PO, ship in OE and invoice in OE.

The only difference is that the inventory is physically delivered directly to the customer and not physically received in your warehouse. But logically you need to receive the inventory in the accounting system to complete the accounting cycle. You can use a DROP location instead of your regular IC location, this way this inventory is kept separate from your regular inventory and the DROP location should have no quantity if all items have been shipped.

I thought this would be the answer, but I am surprised that this is acceptable.

Since there is no drop ship functionality in Order Entry, if you have an order with DROP locations and in house warehouse locations, when you PO is created in Order Entry, is there a way to order only DROP locations without selecting all items?

I have clients that use this all the time, no problems with any one of them.