Chaos-based crypto-steganographic methods for colour images often use a pseudo-random pixel-position generator and a chaotic keystream. However, their behaviour under finite-precision computation is not always examined. In this study, both components were evaluated and two major weaknesses were identified. The modular position generator used in an earlier method could address only 85.7% of the pixels in a 512×512 image. In addition, the 2D Logistic-Sine-Coupling Map (2D-LSCM) was found to produce short cycles for 8.4% of randomly selected keys when implemented with IEEE-754 double precision. To overcome these limitations, an improved crypto-steganographic scheme was developed for hiding arbitrary file types in colour images. SHA-256 was used to derive independent sub-keys from a password and a random 16-byte salt. The payload was encrypted using multi-level substitution and nonlinear S-box diffusion. A perturbed 2D-LSCM combined with AES-256 in counter mode was used to improve keystream security. The encrypted data were embedded using a chaotic Fisher-Yates pixel permutation, LSB matching, and OPAP. The proposed generator and ciphertext successfully passed all 11 verified NIST SP 800-22 statistical tests. The ciphertext entropy ranged from 7.9795 to 7.9990 bits/byte, while a one-bit change in the plaintext, password, or salt modified 99.54–99.68% of ciphertext bytes. Experiments on 1,800 colour images derived from DIV2K showed PSNR values decreasing from 65.9 dB at 0.1 bpp to 55.9 dB at 1 bpp, with a windowed SSIM of at least 0.9989. Chi-square, RS, and sample-pair steganalysis detected LSB replacement but not the proposed embedding on three of the four USC-SIPI covers.