A step before making methane is making hydrogen. If you can get away with just using hydrogen, it will be more efficient than going through the extra steps to make methane.
Hydrogen can be stored underground just like methane can (and is). Also, the problems with hydrogen are overstated. The world economy does use many millions of tonnes of hydrogen each year, so the problems are demonstrably solvable.
2. Methane lingers for decades. Short in planetary timelines. Long in human timelines.
In fact any percentage leaking back to atmosphere (and it will) makes the numbers look pretty bad. You need a significant portion going to plastics or some other sequestered use for this to actually be a net benefit.
2% leakage is very conservative. The amount of additional pipeline infrastructure necessary to achieve this at scale is daunting. It will have a lot of leaks.
If the chlorine is released into the troposphere during the day, it is quickly photolysed (in about 10 minutes at noon) into chlorine radicals, which near instantly react with methane, extracting a hydrogen atom. It should be possible for this to more than make up for small leaks of methane (or to counteract other independent sources of methane).