[advance warning: No snark intended!] :-)
This is sort of tangential to the gravamen of your OP, but...
Can you talk a little about the types of games where this has happened to you? What cards or card-combinations were at play, that resulted in turns where 4+ minutes passed when you were thinking about what move to make?
I can't think of a single game I have played where I thought about what move to make for more than 30 seconds (...this is almost certainly a comment about my overly-casual and substandard play, rather than a comment about your slower and more-considered play.) I am not including, of course, the specific situation of games played soon after a new set of cards is introduced and we're all much slower when we come across a new, complicated, card--but that is not what you're talking about, right?
I'm genuinely curious, and I expect other readers/players are as well. In fact; if players have come across particular kingdoms that are very complicated, I'd bet a lot of players would love to play out those games as well, to see how they would do, how they'd deal with those complicated cards.