Just wanted to chime in since it seems like a few people miss that you put THIRTEENS on it.

Adjusting the claw in the back is what you do when you go from 9s to 10s. We’ve all had to do it which is why that was the advice you were given.

13s coming from 9s or 10s is EXTREME. I don’t have the tension chart in front of me but that is a ton more tension Even at D standard.

Here’s your fix; you need more springs. I didn’t see a picture but I would guess your guitar (like most other trem equipped guitars) only has three springs. For most tunings and string combinations three springs are sufficient.

You are not most string combinations. You need five springs, that’ll address your immediate concern.

However, I reckon you have a couple more issues whether you’ve noticed or not. Depending on how your nut is cut you can generally get away with going up a gauge in strings without too much issue. If your bridge is pulling up that much you’ve definitely gone up more than one string gauge. You’re definitely going to need that nut cut for 13s if you even want a shot at intonation or tuning stability.

I’m sure it’s also in major need of a truss rod adjustment.

Your best bet is to take it to a tech and have it set up. Especially now that you’ve fiddled with the bridge posts. This is the only way to ensure everything is adjusted correctly for the new string gauge. As general rule of thumb you can safely change strings up or down a gauge without too much consideration. Any more than that and the guitar is going to need a complete setup.

For what it’s worth, once setup your guitar should play fine with 13s. I don’t think you have any cause for concern in regards to the guitar being able to “handle” it.

However, adding a couple springs will solve your most immediate concern.