While I have no idea what to suggest regarding an "inconclusive" radon test (beyond more testing), I can tell you what can be done to remove radon. When my family remodeled our home when I was a teen, radon tests were positive in our basement. A special radon mitigation system was installed that somehow pumps radon from beneath the floor up through a pipe and out the roof. While my family has always done a lot of DIY work, this was an area where professionals were brought into make certain the basement was safe for occupation. Personally, I would consider doing another radon test (maybe a different type or brand?) until you receive a conclusive result.

Pricklypearcactus, is this an expensive procedure? I would rather err on the side of caution just to be safe. I know there is radon in our area, and if the basement is a place I'm going to be using, I'd rather not take any chances.

The drain should be part of the "sealed" drain plumbing, so it'll be sealed from the ambient environment under the slab. You won't have radon coming up out of the drain if that's what you're asking.

Pricklypear pretty much nailed it regarding radon mitigation. It typically involves adding perforated pipe under the slab and bringing that pipe outside the house's envelope and up the side of the house to the roofline. A low CFM fan is added to the pipe, it essentially creates a slight vacuum in the pipe under the slab, drawing and radon out and exhausting it to free air outside the house.

If you're going to make the basement into living space that will regularly be used, definitely run more tests. Multiple if possible. Sort of like getting "three bids" to qualify a budget. Radon can change throughout the year. Seasonal, dry versus moist soil, etc. If you have time it's best to test throughout the seasons. Regardless, a long-term test would be more reliable than a short-term test.

Long-term active testing (90 days for example) would be more accurate than a short-term (48-96 hour) passive test.

Sorry, but I do not know the cost of the system. I was a young teen when it was installed and never thought to ask. My mother remembered the tile installers (the whole basement is tile) adding some sort of membrane under the tile. I'm not certain if that may have also provided some barrier for the radon or if it was to protect against water (we have a very dry climate and high elevation). They may have also done something to seal the few cracks in the cement foundation.

I would imagine that your state government might have a list of qualified (licensed?) mitigation experts and information on testing. You could call and ask for quotes. (I called around for quotes regarding asbestos removal and got a per sq feet estimate over the phone.)

Thanks for reminding me that before we finish our basement we need to do radon testing as well.

Thank You both! I'll check into this; it's important enough to want to be safe.