I'll admit, I've never timed a search, so I don't have data about the impact of the rule change. But I do know that we're made an effort to terminate a search earlier than we once would have, so that's positive. I don't have a real problem knowing that during the COVID times, the Tour professionals will have difficulties similar to mine when they hit errant shots, I have very little sympathy. If you want to find it, hit it where there's short grass.
There's no "right" answer, but I'm fine with 3 minutes. I don't think that too much shorter is appropriate, and I wouldn't recommend going back to 5 minutes.
For regular rounds (which is like 90%+ of my rounds) I arrive 30 minutes before tee time. Check in at the clubhouse then spend the remaining time chipping and putting, mainly focused on how the ball reacts when it lands on the green and speed control of putts. Most of the casual courses I play don't have ranges.
Tournament rounds I arrive 60 minutes before tee time, check in and get range balls. I like to take my time and not be rushed for a tournament round. I'll hit roughly 20-30 balls, no specific order, just hitting a few of each "grouping" of clubs like wedges, short/mid/long irons, then fairway wood and driver. If its a narrow course or I know I will be hitting less than driver off the tee, I'll hit a couple extra 3 woods. Then I chip and putt, same as casual rounds getting a feel for firmness of greens and speed.
If you have any Burner driver model from the last 20 years it is going to be .350 tip which means you are out of luck on using in an M3. If you have a TP model then the shaft would be .335 but the shaft you described is not one of those from my memory.
Are you sure it's the shaft specifically that you prefer in the older club? Might want to look at the length, club weight, or swing weight and see if you can replicate the old club feel in the new one. Could also be the head on the M3 you don't get along with.