What you seem to be purporting as a 'simple' (and previously: 'the simplest') explanation seems to me to be complex in comparison to other possible explanations.

I summarise your argument as: "The autograph author of Luke omitted the word 'right' from their account of the Sermon on the Plain because it was not central to the point Jesus was making. Whilst I do not believe that the message of Jesus is substantially altered between the Sermon on the Mount (which includes the word) and the Sermon on Plain (which omits it), anyone who uses the inclusion of this word or other details present in SM and omitted from SP to argue for that the message had a narrower social focus than Luke's editorialised version is wrong."

I presume a few stipulations: SM and SP are two accounts of the same sermon or sayings, written for two totally different audiences, and likely reliant on Q. The SP is an 'epitome' or summary rather than an attempt at an exhaustive recreation of the contents of the document. The inclusion of the word in Matthew's account lends credibility to the fact that Jesus was believed to have said it and that the Q document included it, and the omission of the word from Luke's account does not diminish the likelihood that he said it. These are unremarkable points.

My position is as follows: the simplest explanation for the omission of the word is a transcription error or a later redaction by someone other than the autograph author of Luke, the argument you are having with Winks (via me) is a microcosm of the scholarly consensus around Luke (Jesus was an apocalyptic preacher with a narrow social focus who debated interpretations of local Jewish law in detail, and seemed OK with violence, not -- as Luke would have us believe -- a man who believed himself to be God, knowingly founding a new religion and espoused a message of pacifism) which is at odds with your view, and the position you hold (that we can look to Luke for a more accurate reflection of the thrust of Christ's teachings) is circular (Luke's interpretation of Christ's teachings is both the most widely pervading interpretation and the least compelling from a historical and sociological perspective).

A bit more detail:

The simplest explanation for the omission of the word is unintentional omission. Very common by Bible scribes and nearly always human error.

Until the middle ages, when we see a kind of 'Cambrian explosion' of manuscripts (95% of all extant manuscripts are from after the 9th Century), scribes were barely literate. There are 5600 surviving Greek manuscripts, with in excess of 200,000 differences between them. Many of them are fragments, so goodness knows what the number would be if we had each codex and scroll in full. (This all changed when reasonably educated monks started doing the work.) There are more differences between the manuscripts than there are words in the gospels.

Scribes would often miss out a word, or even an entire line as they laboured to transcribe a document (often in a language they lacked proficiency in). These omissions are more common with words which do not change the meaning of the text (like δεξιὰν, which is the word you're inexplicably fixated on), and unfortunately because of the nature of the formalisation of the gospel canon and its means of transmission being oral history for a very long time, there are likely thousands of words missing from all extant manuscripts which creates the misleading impression that they were never included to begin with. Some we can infer, and some were inferred by later scribes.

It's also possible, and I would argue more probable than the prevailing text of Luke being accurate in its omission, that a later scribe simply omitted the word. P75 is the only extant papyrus to contain the verses we're discussing, but the scribe omitted personal pronouns (as well as Luke's hilarious interpolation of Christ's agony at Gethsemane -- whoosh! Gone! -- and John's parable of the adulteress. Recent graphological analysis dates P75 to the fourth century, which makes it far younger than originally thought.

Similarly P45 (which picks up one verse after the verse we're discussing) is riddled by such omissions. EC Colwell's withering assessment is that it omits "adverbs, adjectives, nouns, participles, verbs, personal pronouns—without any compensating habit of addition. [The scribe] frequently omits phrases and clauses. He prefers the simple to the compound word. In short, he favours brevity. He shortens the text in at least fifty places in singular readings alone. But he does not drop syllables or letters."

So the two most significant early papyri for the of Luke, and the _only_ early papyrus which includes the actual verse we are discussing, both make a habit of omitting words and verses. So if we're to believe that SM and SP are two reflections of the same event, likely sourced from the same documents (Q for Matthew, and Q and Matthew for Luke), we have to pick: do we take Matthew's far more expansive and detailed word for it, with multiple early and later corroborations of the text (24 total, including one which is certainly second century and a handful which straddle second/third century), or do we consider Luke's summary 911 total, of which all are third century or later, and most are heavily fragmented) to be accurate, in spite of the paucity of manuscripts with which to cross reference?