An in-game round of combat is supposed to be six seconds. If a player can't normally fulfil their actions in thirty seconds, the character is "overwhelmed by the flow of combat" and loses their turn for that round. Obviously this would exclude having to pause to look up a rule or two, or for complicated spells.

A rule along the lines of "you can only move your character once" would also help, I believe.

The fact of the matter is that all players should be attentive to the combat as a whole: your problem player has all other players' rounds of combat to ponder what to do next so they should be more than ready to act when it's their turn.