The flight plan in the OP doesn't qualify because it isn't 250nm along airways or ATC vectors. If you take "by directed routing from an air traffic control facility" as including a filed direct route that ATC clears you for, then it would be fine, but I didn't want to have to interpret language in the FARs or dig around for someone who had, so I only counted airways toward my 250nm.
I ended up with a 228nm direct leg to an airport to make an ILS approach, then went missed and flew along airways for 233nm to make a VOR/DME with a circle to land and get fuel, then 79nm along another airway before turning toward the IAF for a GPS approach. After going missed there, we cancelled IFR and flew VFR through the mountains a bit, had lunch, and then headed home separately. I had a really awesome solo VFR flight of about 600nm to get home, although I should have landed three times instead of two and then it would qualify for the commercial solo cross-country as well. All told, I logged 11.2 hours that day, developed a lot of confidence in talking to en route, approach, and tower controllers far away from home, and gained faith in the abilities of the airplane and myself to get from point A to a really distant point B.
If you don't mind building the hours anyhow, my way is a lot of fun. You gain a lot more than checking off the box. But if you do just want to check off the box without an "excessively long" flight, that's probably the more popular way to go. Just make sure that you meet all the requirements so you don't have to do it twice. You must be under IFR on a filed flight plan with 250nm along airways or ATC vectors, you must make three different types of instrument approaches with navigation equipment (which seems to me to exclude precision approach radar), and you must make an instrument approach at each airport. And because it is referred to in the regulations as a cross-country flight and it is toward your instrument rating, one point of landing must be a 50nm straight line distance from your point of origin. The length of each leg and the total length of the flight don't matter. So you could fly 125nm one way via airways, make two approaches, come back along the same airways, make one more approach, and call it good.
By the way, the commercial rating requires three cross-country flights. One must be solo or PIC with only a sleeping CFI as a passenger, 300nm total distance, landings at 3 points, and one point of landing 250nm from point of origin. The other two must be "training" which I interpret to mean with an instructor giving you instruction (mutually exclusive with the solo one, which allows a CFI to be on board but doesn't really call for training. Those are both 2-hour flights a distance of at least 100nm from the point of origin, one during the day and one at night. You could knock out one of those two at the same time as the instrument cross-country.