Is there any theories on putting from the side of the ball so that your dominate eye is forward?  I'm primarily left-handed but have done a number of sports as right-handed.  In my first career in golf, I was right-handed (only ever could borrow/rent right handed clubs) up to about age 30.  Started dabbling again in mid-40's but bought a department store set left-handed and moved on.  Got serious 3 years ago and now use all left-handed clubs.

I've had some issues with a large mallet putter that is also fairly heavy.  I've only gotten close on putts over 10 feet.  From 6-10, a little closer and may actually get one in.  From 3-6 feet, short strokes with the mallet have been an adventure.  The ball will miss left and right.  Left if I don't think about it, and I must be trying too hard to arc/close the head by hand and then I miss right.  I should mention I changed my swing in the last 2 months to keep my arms consistent instead of trying to keep the head on a straight path based on lessons.  I do get a good roll no matter what direction the ball goes.

I spend a fair amount of time at a store working with another mallet, a mid-mallet, and a blade.  The blade was better, the other two were about the same as my own.  For some fun after not feeling like I made progress, there was a used Cameron Sonoma (note it is n/a left-handed...) and I gave it a twirl.  All of a sudden I'm rolling in 15 footers like I've been doing it all my life.  4-5 feet became automatic.

I know that the right correct club for my arc will improve my putting from either side.  Should I expect/assume that with my dominant left eye now forward with putting right handed and reading a better line that I should continue to pursue this?  Clearly with putting, there can be no shortage of desperate times with all the desperate measures other golfers have gone to change their putting.