First of all: this is not something to solve with game rules. As you say, introducing a time limit / punishing indecision definitely seems to make the game not fun and even stressful. On the bright side, it sounds like the player is understanding and willing to try to improve.
They only want to play this one specific character however: a highly intelligent and educated wizard of nobility.
Wizards are a class mired with options - the more spells the worse. However, that also allows for fixing this: reduce the number of spells available (ie prepared), at least for combat. Of course the player should agree with this and perhaps compensated.
For example, instead of a generalist that knows lots of spells, this wizard chose to specialise on just a few - but really masters them. As they are noble, picking some non-compact or social spells is also an option.
We try to not meta-game during combat
This might contribute to indecision too, specifically when it comes to deciding whether to burn the big spells or stick to cantrips. Personally I believe that giving hints that this is the final fight (or the players realising it on their own) is fair game; but divination spells are also something that could be used to justify this.
Finally: spellcards Spell descriptions are extraordinarily verbose; I find that I can summarise most spells in a few characters. Eg fireball can simply become: 20ft sphere, 8d6 fire, DEX halves. This can greatly reduce the time spent scanning - and you can even highlight the saves. Preparing those also feels like being a real wizard!