word choice - difference between しきりに or しきりと?

While looking up the meaning of 頻繁{ひんぱん}, I happened to notice that one of the definitions quoted by デジタル大辞泉 states:

しきりに行われること

However, there's also an entry for しきりと (same しきり as the first, I assume, but with particle と instead of に)

繰り返し何度も。ひっきりなしに。たびたび。

Both definitions sound similar--repeatedly or continually--but is there a difference in usage between using しきりに and しきりと?

Answer

According to デジタル大辞泉, the na-adjective しきり is ナリ活用:

しきり【▽頻り】 の意味
［形動］［文］［ナリ］《動詞「しき（頻）る」の連用形から》
...

So it originally conjugates to its 連用形 (continuative form) しきりに, but しきりと is also used. 明鏡国語辞典 lists both しきりに and しきりと(redirecting to しきりに, so they have the same meaning) as 副詞. I think しきりと sounds a little more casual/colloquial than しきりに, just as the pairs 意外に/意外と, 割に/割と, やたらに/やたらと, 自然に/自然と.