[zeveb]

The cypher you describe sounds like a weaker version of a Vignère cypher, which resisted cryptanalysis until 1863, after nearly three hundred years of use. The Wikipedia page has a decent description of how to cryptanalyse that sort of polyalphabetic cypher.

[Analemma_]

You're right, it looks like my scheme is equivalent to a Vignère cypher with "ABCDEFGHIJKLMNOPQRSTUVWXYZ" as the key, with the weaknesses thereof. Thanks!

[bdr]

You might be interested to read "Cryptanalysis: A Study of Ciphers and Their Solution", a 1939 (!) book by Helen Fouché Gaines. It covers a lot of these kinds of variants.