I planted this maybe 5 years ago. It is now about 6 feet high and maybe 5 feet wide and has a certain charming wild look. I have never pruned it and when I recently did some research I see I should have been removing 1/3 of it branches every year. Bad on me. It is healthy and happy, but has fewer blossoms now than first 2-3 years.
Any suggestions on how I might proceed now? I know it blooms on old wood so I don't want to just sheer it off at the ground.
Take a few older stems out each year, right after flowering. You shouldn't appreciably reduce flowering the following season that way, and that timing will give most of the growing season for the plant to push out new stems. The "1/3 rule" is fine, but I think you can take out fewer if it suits you. As long as stems/trunks are productive, keep 'em.
I don't know any Philadelphus that isn't charmingly wild. None take well to shaping, except maybe some of the dwarf forms that grow in a denser more uniform outline. They are often best used in a mixed shrub border where their charm is balanced by all their neighboring plants.
The 1/3 rule is the rule of thumb for cutting back when a plant is overgrown and you're not sure if it's one that can be rejuvenated by chopping it all the way back (or if you know it's one that won't respond well to that treatment). If the plant isn't overgrown, there's no requirement that you prune out 1/3 of it each year. Since it sounds like yours isn't performing well then it may be time to do some pruning, but don't assume that you will necessarily need to prune out that much every single year in the future in order to keep it happy.