This is a totally reasonable approach. Thought I'd throw in my method for this as another option.
I hold the club sticking straight away from belt buckle or so, parallel to the ground, with my right hand. Then, with my hand splayed out a bit (not crazy stretch or anything, but not fingers touching) and flat, I choose an angle to hold my left hand, place the handle in the "right" position, so resting on the middle section of my pointer finger, resting on or a touch towards the wrist from the bottom knuckle of the pinkie finger. Then wrap the fingers onto the handle, then roll the hand towards the handle to a comfortable spot.
For me this method gives a consistent grip, and I can control strong/weak just by the angle of my left hand before I place the handle. If my left hand plane is perpendicular to the ground, I'll get a super strong grip, too strong. With the left hand plane parallel to the ground, I'll get a weak grip, probably too weak, though for me I don't think it ends up as overly weak as the perpendicular way ends up over strong.
If I have time tonight maybe I'll take some pics to make this clearer...
Like I said… your tempo is probably too slow if you can't get a 30-footer to the hole on slow greens.
You're not hitting a lot of greens, so even two- and three-putting that often is not a great sign. You're not often putting from 40 feet away like some people who hit more greens. You're putting after a chip or a pitch shot more often, and those tend to be shorter putts.
Start a Member Swing topic or post video of yourself hitting long putts to it if you have one already.