It is NOT required that handguns go overnight. That is not if you use a FFL to ship. Assuming that you have a good relationship with your local FFL dealer they will usually ship for free your handguns for you if you pay postage. Shipping from your FFL to Tripps (who also hold a FFL) using USPS PM is about $10 plus insurance. My FFL does this for free because I am a loyal customer but some may charge shipping fees and maybe a little for logging it into their bound book, but most don't. And no, since it is being returned for "repairs" you do not need to do another 4473 when it comes back.
So, take your pistol down to your gun shop and ask them if they will ship it USPS PM to Tripps. You pay the shipping and insurance and have Tripps return ship it the same way. Cost goes from $50-$100 round trip (which is normal for O.N. shipping using UPS or Fed-Ex) down to about $30 including insurance.
And there are no forms to fill out. The FFL fills out a one-page or less form or states that it is a handgun going to another FFL but the owner does not have to fill out anything. Our shop returned guns all the time to manufacturers for repair or other stuff if the gun was bought in our shop and we certainly did not have to fill out a lot of forms. Log it into our bound book, send it out USPS PM and do their form, which is not much, and then when it comes back log it out when the customer picks it up. It is not a big deal. If the gun was bought in our store we shipped it for free and paid all shipping and insurance.
It pays not to be a stranger to your local FFL dealer.