Personally, I think you're on the right track, but I tend to think it's not quite that simple. Specifically, I suspect that the "proximity to SG" limitation isn't strictly a function of distance.

We know, for fact (from Q&A), that proximity to SG IS a factor. Here is the quote:

Q: He [the DO] doesn't have access to all souls to be able to grab any soul?

Jordan: No, no, no. Because of the Bore and the fact that the Bore is best perceived, the Bore doesn't really exist in Shayol Ghul, the Bore exists everywhere, it's simply in Shayol Ghul where it can be perceived most easily. By the same token he has greater access to people at Shayol Ghul than he does elsewhere, or did, and uh, that's, when you know, Rahvin died, Rahvin is balefired out of time, slain out of time, cannot be reached, gone. Be'lal, (names someone else).

But all we can conclude from that bolded comment is that dying "at SG" is different from dying "not at SG". We don't know from that comment if "not at SG" is a function of distance or not.

The "or did" caveat at the end of the bolded part suggests to me that as more Seals weakened/broke, the DO's ability to grab souls away from SG increased, because his ability to touch/affect the Pattern increased.

I suspect, ultimately, that the underlying issue RJ was trying to get at is ... how quickly the DO can locate the soul in the Pattern. Clearly, he can locate it VERY quickly if a minion dies at/near SG - I would guess anywhere in the Blight (i.e. anywhere within his immediate sphere of influence), which would help explain how he caught Aginor & Balthamel's souls when 6 of the 7 seals were still intact at that time.

But when the death occurs outside the Blight then other factors become more relevant. Perhaps physical distance from SG is one, but I suspect there are others, too. For example, I suspect the Shadow's influence at the place of death is a factor. What I mean is, if the Shadow has significant influence at a particular place, or even better, has defeated the Light at a particular place, then I suspect the DO's influence there is strengthened (considerably, in the latter case), making it easier for him to find souls there (within the window of opportunity). Conversely, if the Shadow has little/no influence at a particular place, or even worse, if the Light has defeated the Shadow at a particular place, then the DO's influence there is weakened (considerably, in the latter case), making it more difficult for him to find souls there (within the window of opportunity). Similar to how the Blight retreated after Rand and the Light's victories in/near the Blight at the end of TEotW.

So in Asmodean's case ... he was definitely outside SG/Blight when he died, so that was a factor. And, he died in Caemlyn just after the Shadow had suffered a major defeat there (namely, Rand taking control of the city from Rahvin after killing him). I think that also was a factor. And, like you, I think a small amount of balefire was used, so that was also a factor (explaining, as you said, why HOW and WHERE were both factors).

In Ishamael's case, he was outside SG/Blight, and in a place (Tear) where the Shadow had suffered a major defeat (namely, his own death plus Bel'al's death and the resulting loss of control over the city to the Light). But, Ishamael was channeling the TP at the time he died, and I suspect that "link" to the DO overcame the negative factors that were similar to Asmodean's situation. Plus, he also died in TAR, and we don't know if that was a positive, negative, or non factor in the DO's ability to catch the soul.

Etzel's argument that RJ's quote about the DO still being able to capture a soul if a small amount of BF is used means that the DO can ALWAYS capture a soul when a small amout of BF is used (i.e. other potential negative factors are eliminated in that case) is flat out wrong. All RJ was saying was that if a small enough amount of BF is used, then there is still a window of opportunity for the DO to capture the soul. But, there are still other negative factors that could prevent the DO from capturing the soul in that case, just as he said there are if no BF is used. Why should those "other factors" be eliminated if small BF is used? It makes no sense, and it boggles my mind that Etzel chooses to interpret it that way. If anything, other potential negative factors should become MORE relevant when a small amount of BF is used, because the DO's window of opportunity will still have shrunk some in that case, thereby increasing the probability that other negative factors play a role in preventing the DO from capturing the soul.