namely how no matter what date you set on the sales order, the invoice record will set the ship date field to today’s date

I believe you can set up the default expected number of days of shipment in Setup>Accounting>Shipping. Once the Item Fulfillment is created (shipped status, I think), the actual ship date shows up on the SO beside the expected ship date. Aside from defaulting, I am not sure how it affects other stuff though.