I found it on the Internet, but the explanation I found was a little vague. Basically, it seems that ”しめ” is a kind of colloquial suffix that can have varying meanings depending on the rest of the sentence. However, with the addition of ほど, it seems as though it has the nuance of "almost". So, this is my idea for you. I hope it is helpful. Good luck!!!

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Note added at 54 mins (2008-02-29 01:52:42 GMT)
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I just talked to a Japanese friend and she said that "しえ" gives the nuance of something being like "the last word to say about something" and that it gives a kind of strong feeling almost like an order.

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Note added at 1 hr (2008-02-29 01:59:20 GMT)
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Here are some examples I found. I hope it is helpful.

このころには皆の食欲もほぼ満たされ、教授がブルーノのために四切れ目のプディングを注文したとき、こう言わしめたほどだ。 BY this time the appetites of the guests seemed to be nearly satisfied, and even Bruno had the resolution to say, when the Professor offered him a fourth slice of plum-pudding |
だが、販売数量は伸び悩み、6月に会長兼最高経営責任者(CEO)に就任したネビル・イズデル氏をして「明らかに、まだなすべきことがある」と言わしめた。 But tepid volume growth led to a declaration by Coke's new chairman and chief executive that "clearly there is still work to be done."
ワッサースタイン氏は就任以来、投資銀行部門トップなど優秀な人材の採用と引止めに多額の資金を注ぎ込み、デビッド・ワイル氏やすでに辞めた創業メンバーに利益の浪費、と言わしめた。 Mr. Wasserstein has spent lavishly to attract top investment bankers since his arrival, leading Mr. David-Weill and a group of retired partners to say their share of profits has been squandered.


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Note added at 1 hr (2008-02-29 02:02:41 GMT)
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OOPS! In my first note, I meant to type "しめ”. Also, my friend said that this is not a construction that is used much recently, like Mariko said, but it seems to be found mostly in written explanations.