Can you take a corrective dose of your fast acting insulin to bring your BG down?
This is what I would do in your situation and continue to monitor more often then usual until you take your next basal (slow release insulin) taking care not to over correct or correct too often.
If you take more basal insulin, you risk having too much on board when it overlaps with your next scheduled dose.
I have never read about reducing basal (slow release) insulin when fasting and have never done so.
In fact, as basal insulin dose is unrelated to your diet, I am very surprised by this advice.
However, I find there is always something new to learn about diabetes so would be very interested in thoughts from others.