It sounds like you are printing at the lower end of the possible temp range (no stringing, good bridging). Going 5 to 10° higher should do it. Also, a temp tower will not harm in itself if you are aware of the speeds used in the tower and for the actual print. Better to know and not need than not to know but need. 
There are also quite a few discussions in the forum which may help with PETG. This one includes a bunch of further links.
Hope it helps 
PS: Speed is an issue. Going faster can mean that you have to increase nozzle temp. But for complex parts with overhangs, you need to print cooler and hence slower.