6 of 7 remove extra negation

What you are asking is a straight application of Format Preserving Encryption, which builds ciphers which input and output are in a constrained format (generically: common to input and output, hence preserved). The FPE field has many articles with proven techniques; and proposed standards, including BPS and SP800-38GÂ Draft.

Note: the method tentatively used in the question is not Cycle-Walking, and I do not see that it can be made to work if the cryptogram is kept of the form aes_ofb_encrypt(data); problem is, if the encryption algorithm made more than one try, the decryption algorithm will first make a decryption attempt that does not match anything that the encryption side made, and will occasionally conclude it reached the original plaintext, when it did not.

Here is a minimal solution (for integers of arbitrary size), using a simple variant of CTR (or OFB) mode.

Let $$[A,B]$$ be the interval (assumed public), and $$k\in\{128,192,256\}$$ the bit width of the AES key. Let $$W=1+B-A$$ be the (positive) number of integers the interval. Let $$n=\Big\lceil{\log_2(W)+2k\over128}\Big\rceil$$ be the number of 128-bit blocks to encode $$W-1$$ in binary plus $$2k$$ extra bits.

We'll define $$X\bmod N$$ as the unique integer $$Y$$ with $$0\le Y and $$X-Y$$ multiple of $$N$$. We'll assimilate integers and bitstrings using big-endian convention.

From the $$IV$$, let both encryption and decryption generate a bitstring $$S$$ of $$128n$$ bits by enciphering $$(IV+j)\bmod2^{128}$$ for $$j$$ growing from $$0$$ to $$n-1$$, using the AES block cipher (equivalently: by enciphering $$n$$ blocks of zeroes in AES-CTR mode; using OFB mode would also work though not equivalently).

Given the plaintext $$P$$, let the encryption procedure output ciphertext$$C=((P-A+S)\bmod W)+A$$and given $$C$$, let the decryption procedure output$$P=((C-A-S)\bmod W)+A$$ Trivially, ciphertext is in the desired range, and plaintext is recovered by the decryption procedure. $$S$$ is indistinguishable from uniform on $$\{0,\dots,2^{128n}-1\}$$, thus $$S\bmod W$$ is nearly uniform on $$\{0,\dots,W-1\}$$, with a very slight bias towards values below $$2^{128n}\bmod W$$, but so low that the adversary gains negligible advantage.