When is a word not a word? When it’s an allative suffix, you say, and who could disagree? But this (–)δε is normally reckoned an enclitic postpositive, and who knows how to treat those? Should we write e.g. ὥσπερ or ὥς περ? It’s something of a false dilemma, I think, given ancient Greek writing practice, which doesn’t distinguish between them. It’s only modern editors (and lexicographers!) who have to decide whether something is a word in its own right or not, and interpose gaps accordingly. Lexical status is more of a sliding scale than an either/or thing.
How did the poet view it? Ηe must I suppose at some level have been aware of it as something tacked on to the end of certain words to indicate direction towards, comparable with –θι and –θεν. But if you asked him what the function of –δε was, I doubt he’d have been able to tell you. He knew how to use it all right, but it was just something he’d inherited in certain locutions. And if you asked him if it was a separate word or not he’d look at you in total bewilderment (provided he paid you any heed at all).
You point to e.g. χαμᾶζε, and e.g. οῖκόνδε does indeed seem on some sort of a par with that (though οικον is a regular accusative). LSJ doesn’t actually say “better οἶκον δέ” (I found that startling, and checked) but reports that for Apollonius Dyscolus. I haven’t looked up the cited passage, but he was an outstanding grammarian. Perhaps (I’m just guessing) he held that the δε wasn’t enclitic and should be treated like any other postpositive. There may be Herodianic scholia too.
But we, unlike Ap.Dysc., know that this –de appears to be allative in Mycenean. Unless there are occasions in Homer where the δε is separated from its noun by something else (which is conceivable in principle, but doesn’t happen?), I don’t see why it shouldn’t be treated as an allative relic in alphabetic Greek.
As for discrepancy among editors, that just reflects the confused situation. It looks as if Perseus follows an edition which followed Ap.Dysc., while the OCT didn’t. Myself, I side with you. Given the orthography of e.g. χαμαζε, inseparably merging ς+δ (if that is what in fact it does; but the analogs do, e.g. Αθήναζε), and its (pre)history as an allative, I don’t see good reason to sever this δε under any circumstances.
I don’t remember what Martin West’s practice is in his Teubner edition of the Iliad (which I don’t have to hand), nor whether he addresses the question in the preface (which is the go-to place for Homeric orthographica). If he does, heed him, not me.