'If I could locate' only makes sense as past (because of the next clause and 'no luck') so your rephrasing is correct.

The original version is poorly worded and requires rereading to understand. The easiest fix is reword it with a phrase such as “since I couldn’t find the original nest, I decided to build one.” Alternatively, a type 3 conditional keeps the original sense. For example, “if I had been able to find the nest, I might have been able to put the chick back.”

The original is wrong — your version is correct (this is the 3rd conditional). Also note that “My next work” sounds wrong to me — the intended word is almost certainly the countable noun “job”, not the (usually) uncountable noun “work”.