I wouldn't wait an additional two hours for public transpo. IIRC, the drive from SIN to GH isn't very long.
You will not be able to use TPR.
You only have access to Private Room if (1) you're flying out of SIN on F, or (2) you arrived into SIN on SQ flight on F and have a connecting flight on SQ (whether it be F, J or possibly even Y). If you're PPS Solitaire, you're entitled to use the Krisflyer First Class lounge on arrival, regardless of whether you're taking a SQ or non-SQ flight subsequently.
Otherwise, if you're PPS or have other Star Alliance status, you're entitled to use the Star Alliance lounge, but not the Krisflyer lounge itself.