You can make a virtual ground. It's basically just a class-AB stage that drives the virtual ground. But it will be power-hungry. You will at least double (likely worse) the current draw on your battery to get it done. You may be able to find good ICs that take in a single supply (9 V) and are efficient switchers producing regulated split rails. I have not looked for them so would have to spend time I'd rather let you spend, looking. But I wouldn't be surprised to find some. The double 9 V battery solution is attractive, except as you suggest the +/-9 V exceeds allowed rails and so needs more.
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