Of course not every single instance of ego eimi is theologically significant. But the absolute use of this phrase (i.e. when it does not introduce a predicate such as "I am the bread of life," John 6:35) has only one natural meaning, "it's me" (e.g. 4:24; 6:20). Otherwise it strikes a Greek reader as strange, and I believe it is meant to do so.
As to 8:58, the natural way to express the past tense which the contexts calls for is the imperfect (which is used in 1:1, "the Word was..."). Using the present tense instead is quite remarkable. Other unnatural uses of ego eimi are 8:24 and 13:19 (8:28 is slightly more natural at it can be read as an identification to the "Son of Man"). 18:5ff would be quite natural ("Who are you looking for? -- Jesus -- It's me") were it not for the dramatic effect in v. 6 (when he says ego eimi, they fall down).
So it seems quite obvious to me that ego eimi is a theologically significant expression in the specific context of the Fourth Gospel.Necessarily so in the above instances, and potentially so in other cases -- in the latter introducing a possible double entendre, which is a characteristic device of the author (cf. the well-known case of "being born again / from above" in chapter 3, where Nicodemus misunderstands "again" when Jesus means "from above").
As to what it alludes to, I already suggested that it is rather the similarly striking absolute use of ego eimi in Deutero-Isaiah and a couple of other OT texts as a divine self-affirmation (translating the Hebrew 'ani hu') than Exodus 3 (where ho on, not ego eimi, translates the absolute use of 'ehyeh).
(Editions because of the "error" messages I keep on getting when I try to use italics and the like.
Hmmm... seems to be one particular letter I use in transliteration. Can't write it of course.)