10 gallons are a good start. That's enough to get up to SLAM and see how quickly you go through it. And then buy more. Every SLAM is different, you have to go with the flow. The more often you check and get back to SLAM level, the faster the overall process, but there's also no point in getting paranoid. I would check one more time once it's dark.
In your case with limited reagent access and relatively high SLAM level, I would even consider using a 2.5ml sample (measured with a syringe) and have 2ppm per drop resolution for the test and dose. Just assume for the dosing that FC is 2ppm lower than you tested to calculate the next chlorine top-up. You might overdose slightly, but wasting a bit of chlorine is in your situation better than running out of reagents mid-SLAM, I'd say. Or make a 50:50 mixture of pool and rain or distilled water and take a 5ml sample of that to get 2ppm per drop.