Accuracy concerns with a tighter base pin
My thinking goes like this (but for the thirty bucks for a new base pin and a borrowed machine rest, you can confirm or deny all of this yourself -which I kind of wish you would do and then I'd be taking YOUR advice);
Any change or rework that tightens up the lock-up should only be done if you intend to bore out and convert a gun to a larger caliber with a smith who line bores your cylinder. This is because the slight bit of 'play' might be necessary because that is the only thing that is currently permitting your gun to shoot well. In other words, you might have slightly out of line chambers which gets corrected because you have play. Take away any of that play and the misalighnment now hurts your accuracy.
Like the previous posters say; work up your loads with commonly accepted practices and safety and see where you are today and go from there.
I couldn't believe how my groups were affected because I was not concentrating on absolute consistency of every aspect of handgun shooting. It is amazing and a fascinating challenge that can take (for me at least) years to meet in order to truly be able to say "This is my potential" and distinguish this from your overall group size which would then give you your gun's potential. Of course you can shortcut this if you need to know today whether or not you have a lemon; just invest in a machine rest I guess.
I personally found that with heavy loads, my base pin was moving because the base pin latch was getting mushroomed. And even here, a stronger base pin latch spring cured that. I do plan however to invest in an aftermarket, hardened base pin latch and that's about it. But my Old Model seems quite accurate, and I have plenty of play in the cylinder but I am not going to do anything about it.
Good luck.