I think it would be important to take a closer look at the student's behavior when taking an exam (or possibly in individual practice problems). Where are they losing time? Are they just globally slow at everything? Or are there particular operations that cause them to lose time? Slowness may just be a symptom of a deeper problem that needs to be addressed.
I can illustrate with two related anecdotes.
Even in 3rd grade, I hated memorizing. I stubbornly refused to memorize the multiplication tables since multiplication was taught as just repeated addition. If I could translate my thoughts back then into my vocabulary today, my attitude was "Why memorize that which I can derive from first principles?" But the tests were timed and I failed most tests because I couldn't add fast enough. To this day, I'm irked that the teacher didn't pull me aside and try to understand my problem. She could obviously see the columns of digits that I was laboriously adding in the margin.
Fast forward about 20 years to freshman physics in college. For me, I loved being able to start with first principles (say, Newton's 3 laws) at the very beginning of a chapter, and then being able to prove their consequences (such as the path of a projectile being a parabola). That's how I handled exams. With few exceptions, I would start with first principles, derive the equations I needed to solve a problem, then solve the problem. I failed to finish most exams because I ran out of time. Finally, one day it hit me like a ton of bricks: Oh my god, the professor doesn't want me to understand the foundations of physics. He just wants me to memorize the list of equations in the chapter summary and then mindlessly plug and chug on exams. Once I understood the game, my performance on exams improved.
I'm not saying that "failing to memorize" is this particular student's problem. Only that if you have the time and resources, it would help the student to diagnose the slowness problem more thoroughly. Where are they losing time? If it's global slowness, then (as others have already suggested) drilling is probably the best prescription. But it may be a more focused issue that is causing problems.
On exams, are students expected to show their work? If so, that might be a good place to start to see where they are losing time or going through unnecessary steps.
Have you asked the student for their perspective? You had mentioned that "Talking to them afterwards, it seems that they are constantly under time pressure." I think you could inquire deeper. The exams are timed. They are under time pressure. But we don't know if thefeeling time pressure is cause (e.g., math or test anxiety) or effect (losing time due to some other problem).