At the risk of offending, I will disagree, and ESPECIALLY with this diver. Without trying to brag, as an old diver/instructor/anesthesiologist whose business is airways, I have to gently disagree.
Here's the deal. Without a mask that is almost COMPLETELY empty of water already, what happens when you look "way up"? Air bubbles (in your nose) rise and are replaced by water (in your mask), that then trickles down your nose/throat and increases the very sense of panic that worsened this diver's dilemma.
Second point: how do divers in perfect horizontal trim clear their mask? They can't look "way up". They stay horizontal, look out at the horizon and clear. The nose cup is the lowest part of the mask, and when they replace all the water with air, the lowest part is dry. There is NO NEED to look higher than horizontal. Additionally, this provides the added benefit of making the nasal passages HIGHER than the nares (nose holes). That means that it keeps this area dry, and keeps panic down.
Since I'm a PADI Instructor, I know it is professional suicide to tell my students that their textbook and videos and pictures are wrong. The pictures and my required training technique is not wrong. But finding that one phrase in the manual or video that instructs the student to look up AT THE END, is hard to do.
I teach my students to start by looking DOWN at about 45° (keeping water out of the nose). As they exhale thru the nose and the mask empties, ONLY THEN do I tell them to look up, and I explain why (to keep drops from trickling back). As soon as they try their second mask clearing drill while hovering horizontally, they realize that they don't have to look way up, they stay drier in their nose and have less panic.
I'm always reluctant to say that a given post is incorrect, but in this case I feel strongly about this technique, and hope I have adequately explained why.
It depends on the shape of the mask to an extent. Some masks will clear completely while looking horizontally, some need a bit of a tilt back or water remains at the bottom of the lenses. I agree that there is never a need for the exaggerated looking to the surface pose.
To the OP. Mask clearing is a core skill. The solution is not a better fitting mask, perhaps it is a worse fitting one. Get used to clearing your mask as second nature. I am a verry lazy person so I have a part beard a lot of the time. This means I have a leaky mask a lot of the time, so I have to keep clearing. I couldn’t tell you how many times on a given dive I clear my mask any more than I could tell you how many times I breathed.
I take in a lot of divers for their first dives. This usually happens in UK quarries with not so good vis and cold to very cold water. These are not good conditions for mak clearing and many to most people have a problem with it. With a hood and gloves, wearing a thick and restrictive suit, it becomes quite a difficult skill. However it is an essential skill, especially so if you dislike water on your face. I will always have a student do this successfully in standing depth before trying it at 5 or 6m as I don’t want them rushing for the surface and this is the skill that is most likely to result in that.
If you wear contact lenses leave them in the car. The extra worry and hassle doesn’t help. Keep your eyes open if you can bear it. Practice controlling mouth vs nose breathing out of the water. Know for sure you can exhale through your nose while your mouse is open. Practice with a a snorkel and no mask. Take your time for practice. If it takes two hours to be happy replacing a mask in standing depth then that is two hours well spent.
People who leave initial training fearful of mask clearing often avoid it to such an extent that they never get over it. Don’t be that person, Diving is supposed to be fun, nagging doubts and hoping stuff doesn’t happen isn’t a way to have fun.