Let me first suggest that if you are a type 1 and only using Novolin N, then you would probably do better moving to an intensive insulin regime called MDI. It involves multiple injections, but will enable you to achieve better control. That being said, if you are using N alone, an elevated fasting number in general suggests that you need to increase your dose. If you are already experiencing lows during other parts of the day, then the only option is to move the injection timing to try your “luck” at better matching the peak of N to address your highs.
But my recommendation is to add a bolus insulin and do a full MDI regime. This can enable you to reduce you N levels which have been covering both basal and bolus needs and get better control of things. With using just N, you don’t have enough variables to change to meet your needs. You can use R for dinner, but you need to understand that R peaks over 2-5 hours and can last up to 8 hours. If your N dose is already bringing you down to proper levels at bedtime, taking R at dinner may give you lows at night. .