VISCII went for the last option, replacing 6 of the least problematic (e.g., least likely to be recognised by an application and acted on specially) C0 control codes (STX, ENQ, ACK, DC4, EM, and RS) with 6 of the least used uppercase letter/diacritic combinations. While this may cause issues with some programs in handling VISCII text if they use those control codes, it creates fewer complications than either of the other two solutions. However, it leaves absolutely no space available for things other than accented letters such as symbols, superscripted numbers, curved quotes, proper dashes, etc.
It's developed in 1992 by Vietnamese Standardization Group (Viet-Std Group) from TriChlor group in California and is officially registered as ISO-IR-180. VISCII, along with other Vietnamese-specific character sets, fell out of usage with the adoption of Unicode.