To be honest a PID won't resolve the issue. Fundamentally the boiler is too small. Each shot you pull is taking a significant volume of water out and it cools too much. A PID can't accommodate this inconsistency - all it does is a more accurate tempeature surf. When I had a Silvia with the auber PID the temp would drop by approx 10 degrees over the course of one shot being pulled. You can imagine what subsequent shots would do.
To be honest a PID won't resolve the issue. Fundamentally the boiler is too small. Each shot you pull is taking a significant volume of water out and it cools too much. A PID can't accommodate this inconsistency - all it does is a more accurate tempeature surf. When I had a Silvia with the auber PID the temp would drop by approx 10 degrees over the course of one shot being pulled. You can imagine what subsequent shots would do.