I'd say that schon modifies mal modifies verpacken. schon mal is adverbial of time, basically gleich, bald (soon, not strictly immediately) and it carries a sense of colloquialism denoting a simple task, so simple that bitte would be too formal, though bitte schon mal would be a compromise. So, for imperative speech, it leaves a choice of when the action has to be done, but it is usually accompanied with a constrained "... bevor ich zurück komme". In that sense, schon mal is almost redundant. "Bitte verpacken Sie das, bevor ich zurück komme!" or just "Bitte verpacken Sie das zeitgemäß" (in due time). However, it can also stand on it's own. The sense bevor becomes very apparent in "Ich habe da schon mal was vorbereitet" (I have [already] prepared something), thus also "Ich werde schon mal etwas vorbereiten". Your observation, that "do that already" sounds denigrating is not completely wrong. On the one hand, if not accompanied by a time limit, one is left guessing and the implication is to do it rather sooner than later. On the other hand, it appears in the accusation "Das hättest du schon mal tun können" (you could have done that already). Note that bereit carries over very well to ready. In fact, bereits exists: "Du kannst das bereits einpacken".
schon on it's own means already, yet. "Ich habe das schon gemacht".
mal, Mal designates a time and is largely synonymous with einmal (once), and perceived as a shortening of that. Although, of course, it also appears in zweimal (twice) and the like, only einmal stands in for a time. "can you pack that once yet" doesn't have the right ring though .
Under influence of einmal (irgendwann "unspecified time"), schon mal expresses a restriction on einmal, ie. schon einmal, which exists in the same sense, and, if not for syntactic or logic reasons, the ein is simply contracted and elided "schon'nmal". In that sense, it should be written as a compound, as are beidemal, vielmal, niemals and the like; wiktionary indexes colloquial schomma and schonmal, but Duden-online does not.
Since -al is an adjectival (noun-)suffix from Latin -alis, I'd presume that -al is short enough to be perceived as a suffix, as if GEN beidem+-al. I'm not aware of an etymological tangent along those lines, but at least a phonetic argument could be made. "Kannst du da mal gucken?" just flows better. Edit: I guess dezimal would be an example of this, where the common prefix today is dezi-, but the m comes from Lat. decem.
A contrived, but helpful translation would be nicely, since schon apparently derives from schön. "Kannst du das schon mal schön verpacken?" wouldn't be unheared of, and that's where the stark contrast to "already" becomes apparent.
Still though, the sentence could be transformed for clarity.
a. (Du (((kannst) schonma) ((das) verpacken))).
(You ((can) already) (pack (that) up)).
Whereas "Du kannst das schonma verpacken" would be a bit closer to "damn already", but I'm not firm with syntax tree building.
Also helpful might be an analogy to einfach, zweifach (one times, two times) and einfach (simple), thus: "You can pack that up, easy".
: On that note, you have to wonder just a bit about jetzt (now, viz gleich, bald), which sounds like a mix of yet and the -ce in once--yetce :D but je has a very difficult history. once stems from a genitive construction; jetzt is amenable to a superficial analysis of je + zu; Dunno if that zu marks the genetive. de.wt/jetzt mentions "Ursprüngliche Bedeutung wie heutzutage", thus we may think of *schonzumal, comparable to dazumal or just zumal. Compare also zubereiten and the like.