What you want to do is get a dedicated pair of glasses for sitting at the computer. And, don't let them give you any bull about, "We just have to measure you for distance and reading, and can calculate it from that". Get a tape measure (one of those cloth ones used by tailors works great) and measure how far away your screen is from your eyes is as your normally sit. Do this a bunch of times over a few days to make sure it's accurate. If you also use a laptop, measure that distance too (in whatever posture you normally use your laptop). You may find it's not the same as your desktop. It might help to enlist somebody to help you make these measurements.
Then, tell your eye doctor to measure your eyes for that distance. The standard machine they use can do that, they just don't like to do it because it takes more time. There's a calibrated rod that attaches to the phoropter (that's the Rube-Goldberg thing you look through with all the dials and lenses), and a card they can hang from that at any specified distance. It's called a near-point scale. The doctor should set that at whatever distance you measured for your workspace.
Next, make sure the doctor writes a specific prescription for this distance. Again, don't let them give you any crap about how the optician will figure it out from your distance and reading Rx's. All the optician will do is average them, which may be good, or it may not be. Insist they do it right. If your doctor isn't willing to take the time to do the exam right, vote with your feet. Many doctors won't want to do this because it takes more time, and time is money.
Then, have a set of full-vision glasses made up with that intermediate prescription. Use them. Keep them at your desk if that's more convenient than carrying two pairs of glasses around with you.
I found progressive lenses horrible. I went through a few attempts, and eventually settled on old-fashioned bifocals. The kind with the line in them. In addition to the full-vision intermediate lenses described above, I have a pair of bifocals made up for my exact use-case: being able to see the whiteboard or screen in a meeting, and still be able to work at my laptop. To do that, I have my distance Rx in the top, and my *intermediate* Rx in the bottom. I also had them drop the line between these a little, so I really have to look down to see through the lower part. And, the lower part is also a little wider than the standard area. It's exactly what I needed. The thing to realize is they can make up any combination of lenses to fit your exact need. Car mechanics often have bifocals made up with the near-vision lens on top (so they can see what they're doing when working under a car on a lift). It's called occupational lenses. If your optician isn't willing to work with you to make you exactly what you need, again, vote with your feet. PS, some vision plans will pay for occupational lenses above and beyond the regular benefits.