I purchased a GSR200 a few years back for the daughter of a family friend, and it had the same issue with balance as you described. It's most likely due to the standard scale solid Maple neck being attached to a relatively light Agathis body, which has a fairly big electronics cavity, given the stout electronics package. The solid die-cast tuners on the headstock aren't helping anything either. There are a few cheap and easy fixes that will help you solve this problem without doing anything permanent to the instrument.
You can do one of any combined of the following:
1) Roll some coins in electrical tape and put them in the control cavity to act as ballast. Essentially making the body heavier.
2) Use a thicker (width) strap made of leather, it'll have more friction on your body, and thus stop the bass from diving as easily, compared to a thin nylon strap.
3)Play with the strap higher up, it brings the bass closer to you giving you more control.
As for the more expensive SR series basses, such as the SR500 and SR600 there is no balance issue, at least from the examples I have played. That's due to the thinner, lighter necks and the heavier bodies made from woods like Mahogany, and Ash.
Current "Heard":UV777PBK - UV7PWH - UV7BK "Green Dot" - UV7BK "Green Silver Dot" - RG7620VK - RG7420BK - RG1527RB
GUITAR SET-UP AND MAINTENANCEIbanez Catalogs---
Megatron's Trem GuideNeed replacement parts? Go here.Want to talk to Ibanez USA (Hoshino USA)? Then call this number (PA area code): (215)245-1648.OFFICIAL IBANEZ PARTS & APPAREL STORE!!!