Is this the correct procedure for cycle walking using an FPE?
Yes, what you're describing is the correct way to cycle walk with FPE.

In your case, the value you're encrypting is ten bits, so the largest possible ciphertext is 1024. You'll only need to cycle walk if the ciphertext is from 1000-1024, so 24 of the possible 1024 values will cause an iteration. This means your probability of cycle walking for any particular value is $\frac{24}{1024} \approx \frac{1}{40}$, which is pretty small.