I had a similar issue with a cheap Gretsch I bought on EOY closeout, Dec 2024. The adjustment screws were maxed out on the OEM bridge. In my case, the low E was the worst offender, G was 2nd worst. Theoretically, longer bridge adjustment screws could have solved the issue for me. However, I opted for a replacement bridge.
Truss rod adjustments will affect intonation. So, if you can’t get the intonation correct with the OEM bridge, it could be that there is either too much or too little relief. Sorry, I forget which situation causes sharp vs flat.
String gauge directly affects relief and the truss rod. So, different string gauges will change the neck relief and change the intonation. Heavier strings cause the neck to have more relief and lighter strings cause less relief. I’ve even experienced bad quality, new strings that throw intonation off.
Action can affect intonation. So, I suppose changing the action could, theoretically, improve intonation. But, I would never use that strategy. It is a known problem that super high action will make it difficult to set proper intonation. However, I want my action set where it feels best for me period.
My guitar setups always start with my preferred (1)
strings based on the guitar’s scale length. Then, I adjust the (2)
truss rod. Because, I use light strings, the truss rod is often at the lowest tension, or very near it. Next, I set the (3)
action which is different depending on the specific guitar. I want all the notes on the neck to ring out, so my action tends to be a bit higher than OEM specs. The more perfect the neck and frets, the lower the action can be set. Obviously, a fret dressing can improve the situation. Last, I set the (4)
intonation at the bridge with a Strobe Tuner. If you don’t have a strobe tuner, there are strobe tuner apps available on smart phones.
Here is my Gretsch showing the OEM and replacement bridges…
