Is this a contraction along the same lines of なければ → なきゃ?
Also, can you contract 言えば or あれば?
You are asking what や in 大きすぎやしないか is.
I think that it is a colloquial deformation of は, as is explained in this entry in Daijirin. According to this explanation, it was originally 大きすぎはしないか, in which particle は was used to emphasize the part 大きすぎ.
When attached to certain verbs, it is often further contracted as in わかりやしない → わかりゃしない, 聞きやしない → 聞きゃしない. But this is not always permitted, and I do not think that contraction 大きすぎやしない → 大きすぎゃしない is acceptable to many people. (For more detail on when this contraction is accepted, see question “Contraction of や, the variant of は” by sawa.)
The question about 言えば and あれば is a different question. If you want to ask it, please post it as a separate question.
(Before I looked up the dictionary, I was thinking of a different answer. In the classical Japanese, there was a particle や which denotes questioning (疑問の係助詞「や」). It is no longer used in the modern Japanese except in fixed phrases such as …するや否や. I was thinking that や in …やしないか might be this や. However, this is probably not the case because …やしない without か does not have the meaning of questioning.)