Maybe the real pros will tell you something different, but here goes my take.

Do you have an access panel? If so, connect the waste and overflow assembly to the tub, and then drop it in place. Replacing the trap also (unless it happens to be lined up perfectly, which is doubtful) gives you the room to make adjustments. Once the tub is set, glue in the trap to the arm carefully to line everything up. (Dry fit and mark the pipes as necessary before you glue them - that's where you have one chance.)

Quote: " have purachsed and assembled the waste/overflow assembly for the new tub"

You have placed the cart before the horse so to speak, and thereby made a rather simple task very difficult.

You are considering the use of a coupling, which tells me that you will have an access to the space during the installation? Otherwise you would never be able to reach the coupling to tighten it. The question then is, will you have a 12"x12" service access either through an adjacent wall or up from underneath after the job is completed or will this space be completely closed in? If you will have an access panel you may use a conventional "Slip Joint" type waste & overflow kit. The slip joint type kits have telescoping pipes for both the drain line and the overflow riser which allow for easily tweaking the fit, on the other hand, if the space will be completely closed in, you are then required by code to use a "Glue in" type waste and overflow or "solder in" if your code requires metal pipes.

A common slip joint type waste & overflow kit comes complete with the drain line, overflow riser and baffled Tee tailpiece but such may not be the case with a glue in W&O kit. Many glue in type W&O kits supply the Overflow body with trim and mounting components, a Baffled Tee and the Tub shoe with the gaskets, tub basket and stopper or trim cover, depending upon which type of stopper you choose. The pipe for the tub drain and the overflow riser would then be supplied by the installer from Sched. 40 PVC stock.

The easiest method is to first install the tub and secure it in place. From this point it is best to have two people. The lead person working under the tub while the helper works from above.

Begin by fitting the overflow body in place but keep in mind that you will be taking it out again as soon as you get some measurements so you need not install all the final trim at this point.

From the center of the overflow body discharge port drop a plumb bob down to the P-trap area. The Plumb bob is now marking the correct center position for the P-Trap input.

Once you have the P-trap positioned correctly you attach the "tub shoe" under the drain opening leaving it just slightly loose so you will be able to move it while taking the next measurements. (Tub Shoe is the correct name for the casting directly under the tub drain opening that receives the Tub basket).

At this time you will be dry fitting the componentsdo not glue anything yet.!

Insert a piece of sched. 40 PVC stock in the input of the P-trap and slightly longer than the length of the vertical rise up to the Baffled Tee then insert a second piece of sched.40 PVC stock in the output port of the tub shoe and running to the baffled Tee location. Make sure the drain line from the tub shoe to the baffled tee has a ¼" per foot pitch downward towards the baffled tee. Now you can hold the baffled Tee in place and mark the correct length for the tub drain and the baffled tee tailpiece. Pull the tub drain and baffled Tee tailpiece out and cut to length

At this point you can begin gluing the pipes. First glue the tailpiece into the P-trap to form the riser up to the baffled tee. Next glue the drain pipe into the tub shoe Now dry fit the Baffled Tee on the top of the tailpiece so that it can be rotated at this point and glue the drain line from the tub shoe into the side opening of the baffled tee and quickly align the tub shoe with the tub opening to insure the top of the tub shoe will be flat against the underside of the tub. Have your helper prepare the tub basket by putting plumbers putty under the flange of the tub basket and be prepared to screw the tub basket into the tub shoe. Now disconnect the Baffled tee from the tailpiece and place the rubber gasket on the top of the tub shoe where it will contact the underside of the tub. (I like to apply a light film of clear silicone sealer to both the top and bottom surface of the gasket. This will help hold the gasket in place during installation and will aid in getting a tight seal between the gasket and the underside of the tub.) Glue the bottom of the baffled tee to the top of the tailpiece and quickly align the tub shoe to the tub drain opening. At this point your helper can insert the tub basket through the tub hole and screw it firmly into the tub shoe. Tighten the basket with a Basket wrench then install the trim cover over the drain opening.

You can now get a final measurement for the riser from the baffled tee up to the overflow body. Remove the overflow body and cut a piece of sched. 40 pipe to length and glue it into the overflow body. Attach the rubber gasket to the overflow body, (I like to put the clear silicone on both sides of the overflow body gasket also) then you can glue the riser into the top of the Tee and quickly align the overflow body so it is tight against the tub wall. You helper can now install the overflow body, mounting bracket and drop the stopper down the overflow pipe, then attach the final trim cover.

Your done so now its coffee time.

The real challenge comes when you have a tub over a slab and both the head wall and the back wall are outside walls of the building so you have absolutely no access under the tub once the tub is set. In this case you have to measure everything super close and make all the underside connections to your theoretical measurements, then set the tub and pray its all lined up correctly.