Thanks to Dr. Carl Conrad, I've been shown a fatal flaw in the below; I've confused the adjective ἄλλα with the conjunction ἀλλὰ. Now it all makes so much sense! Thank you, Dr. Conrad, for the correction. And for the reminder to double-check parsings before spending too much time trying to figure out something that doesn't make sense.

The below is left as testimony to my folly. When you need a laugh, do please read it again.

Here is Holmes' Greek for the first sentence of IgnEph 7.1, followed by his English.

7.1 Εἰώθασιν γάρ τινες δόλῳ πονηρῷ τὸ ὄνομα περιφέρειν, ἄλλα τινὰ πράσσοντες ἀνάξια θεοῦ·

7.1 For there are some who maliciously and deceitfully are accustomed to carrying about the Name while doing other things unworthy of God.

The above is from his second edition, but the third edition is exactly the same. For some comparison, here's Ehrman:

For some are accustomed to bear the name in wicked deceit, while acting in ways that are unworthy of God.

So as to be complete, here's Kirsopp Lake's translation.

For there are some who make a practice of carrying about the Name with wicked guile, and do certain other things unworthy of God;

The Greek is the same in all three editions, so we're comparing apples to apples. The question is, what is αλλα doing in this statement?

My basic contention at this point is that αλλα is a marker of contrast (as Heckert has posited); I'm comfortable with saying that it indicates discontinuity (which is what Porter and O'Donnell note) but contrast seems the better term, and I really don't see much difference between "contrast" and "discontinuity" anyway. The second part of my contention is that when one encounters an αλλα, one must realize there need to be two parts in order for contrast to be made (or for there to be discontinuity); with αλλα, the latter part corrects/replaces the former part.

My contention, then, is that looking for these two things when examining instances of αλλα is essential, and that if you can do this you don't need to worry about sense-classifying αλλα. You don't need to worry if it is continuative, or adversative, or contrastive, or what-have-you.

Further, particularly in situations like we find here in Ignatius to the Ephesians, the latter part (the correction/replacement) is set up such that it is the more prominent/salient piece of the whole sentence/paragraph. It is the author's primary point, it gives the punch to what he's trying to get through our (well, mine, anyway) thick skulls.

This instance in Ignatius to the Ephesians provides a good example. The standard gloss "but" doesn't fit (mostly because there isn't a negative involved, which would heighten the contrast and make "but" feel more appropriate), so we see some translators use "and" (Lake) and others use "while" (Ehrman and Holmes, though perhaps in these instances "while" comes from the participle and αλλα is left untranslated). But that doesn't really help us to see the contrast (whatever degree of contrast is present is indicated by the context, not by αλλα) or the things being contrasted, and it isn't easy to see what corrects/replaces the other. So let's look at the Greek again:

Εἰώθασιν γάρ τινες δόλῳ πονηρῷ τὸ ὄνομα περιφέρειν,
ἄλλα τινὰ πράσσοντες ἀνάξια θεοῦ

Basically, there are some people who "bear the name" yet while bearing the name (note that this in itself is important to Ignatius, who calls himself "the God-bearer" in his epistolary introductions) they do things unworthy of God. This is the contrast, that they say represent themselves in one way, but act in another.

What is the correction/replacement? It is the same thing, basically. My boy Iggy is pointing out that these evil, nefarious people who claim to "bear the name" are really not to be trusted because their actions betray them. This is Iggy's point: They're not who they say they are, so beware. They should make the hair on the back of your neck stand up.

That this is the salient bit of this sentence is born out by the following sentence. Again, Holmes' translation:

You must avoid them as wild beasts. For they are mad dogs that bite by stealth; you must be on your guard against them, for their bite is hard to heal.

You can see exactly what Ignatius is doing now; paying attention to the discourse cues in the original language helps us understand even better how he got there.

Of all of the translations cited, I'd say I like Ehrman's best. But even then, the αλλα is obscured, and the basic sorts of things that I contend it clues us in to are hard to see. At the same time, accounting for all of that in a translation is hard, and I don't have a better suggestion. So, at the very least, consult the Greek as you read the English. Sometimes you'll be very surprised at how the translator renders what's happening in the original language text. But, particularly with particles and conjunctions, the work pays off.