Consistent steam performance

I recently bought a refurbished Gaggia Classic. It's got several mods, like a PID among others. The PID only manages brew temperature though, it doesn't affect the steam temp. But I can still use it to watch the boiler temp when preparing to steam.

When I want to steam milk, I flick the steam switch. At that moment I see the temp rising to about 150C. When I start steaming at about 140 or something, the steam is violent and short. I get milk all over the place and in the end it's still cold because there just isn't enough steam.

So I wait another cycle. After it hit 150C it slowly creeps back to ~110C after which the heater gets turned back on. When it hits ~135 I start steaming. At that moment I have plenty of power and plenty of steam.

This way I get pretty consistent results, but the problem is that it just takes way too long.

Is there a way I can speed up my workflow?