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As I've treated it, the しな at the end of the sentence is just し("not only, but also")+な(=ね). But Jisho.org says it could also mean "having just started...".
Is this true? Is there an example of this usage?
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「Verb in 連用形{れんようけい} ("continuative form") + しな」
means:
"just when (verb)ing", "on the occasion of", etc.
「しな」 is a suffix in this usage.
Examples:
「帰{かえ}りしなに雨{あめ}が降{ふ}ってきた。」 = Just when I was leaving, it started raining.
「寝{ね}しなにジャズを聴{き}くのが好{す}きだ。」 = I like listening to jazz just when I am going to bed.
