@BigDaddyGlad
Lots of good advice already given...
1. Yes, do the stopover in Singapore. It's the cleanest, safest, (mostly) interesting city in SE Asia. We just did two stopovers in Singapore on our recent trip diving in the Philippines and Maldives earlier this month (just got back last week). Very easy to get around, everyone can speak English (literally everyone), and really (really) good food.
2. Don't spend your layover near the airport. That would be like visiting New York and spending your time in Newark. There are a ton of affordable hotels around the city, and as I said - it's a very easy place to get around. We end up walking most places, just keep in mind that it could be hot (and/or rainly).
3. Some have suggested booking the Garuda flight from Singapore to Jakarta so your bags can can be checked through to Sorong. That is definitely true, however, even after the short flight from Singapore to Jakarta, we always want to make sure our bags make our connection, so we collect our bags in Jakarta, and re-check them to Sorong. That means we can also fly Singapore Airlines to Jakarta without worrying about our bags being checked through. Given the departure time of the Garuda flight to Sorong, you have the time to do this without rushing. SIA was just voted the word's 2nd best airline (Qatar Airlines was #1), we try to fly them as much as we can in Asia - they are just better (service, food, and planes).
4. We've been to central and northern RA several times in June (due to school vacation schedules). The weather is usually fine. On three trips we've never experienced the wind that others have mentioned, but the visibility can be variable depending on where you dive. You will get some rain, but that's true for the entire region for most of the year.
Last - seriously consider eating out in Singapore. The food is world class... their (unofficial) national dish is Singaporean Chilli Crab. It is outstanding...