I am wondering if I get myself a more forgiving putter maybe that will make these putts go in.
I'd say it's not at all guaranteed since the program seems to do a lot NOT to let the putts in. What hurts me most is the "2 inches short" putts!
/methinks that this has no relation to forgiveness.
In general, forgiveness describes the shot reaction on quality defects, i.e. when you miss the ding. The more forgiveness, the less effect it will have compared to a perfect shot. Thus, it's good to have high forgiveness if your putting method includes hitting the ding on every putt.
OTOH, it's poison for the other putting method, "off-ding putting". With this, players miss the ding voluntarily to influence the putting path. If you see a slope, you don't move the marker but click a little early or late to compensate. In this case, low forgiveness is good because you WANT to experience a significant effect on the putt!