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Hmmm, that's exactly the same method I use (except I burn at 16x) and it should work like a charm.
Have you changed disc brand at all?
My own LiteOn LH-20A1H will read/burn CD+G - even though Nero InfoTool says otherwise - so I'd imagine your LH-20A1L should too.
Have you definitely ruled out the JVC acting up? Do you have another standalone DVD player you can try the discs on (I know our Philips models will support CD+G playback).
If all else fails, the culprit could be the LiteOn and you may have to use a different drive to burn them.