My pregame warmup for putting is to putt 4 balls at 90° (ie a cross shape) to the hole. Start at about 2' and work out by a foot each progression. Stay at that same distance until you hole all four balls consecutively.
My game was similar to yours (it has regressed again the past few years sadly) and I usually track driving and approach accuracy and # of putts as a gauge for how well I am playing. At first my putting average was pretty decent, and my goal was to average 2 putts per hole. As my approach game got better (ie I hit more greens) I found my putting average got worse which had me stumped until I realized it was because my initial putts were from longer distance now. When my iron game sucked I was missing the green but my chipping got me closer to the hole than my longer irons were as I began missing fewer greens. That made my putting seem better. Perhaps there is some of that in your game and your putting is not as bad as it seems, you are just starting with longer putts.
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