Looked good to me, then I realized that beutel is pronounced 'boy-tel'.

Yes, but according to Kluge's German etymological dictionary New High German Beutel is related to the following: Old High German butil, Middle High German biutel, Old Saxon bu:del, Middle Dutch bu:del, Modern Dutch bui(de)l, Old West Frisian bu:del; and without the l suffix Old Icelandic budda 'gold-purse', dial. Swedish buda 'head', Old English budda 'dung-beetle, Middle English budde 'bud; beetle', originally meaning 'swollen'. All of which are ultimately from the PIE root *bheu-. (Where V: indicates a long vowel.)

I didn't mean that boodle had been borrowed from German Beutel, but that both were related to earlier words or roots in earlier languages. New High German eu usually goes back to an Old High German iu which in turn comes from a Proto-Germanic u:. If we look at some cognates in German and English, we see how this original vocalic sound gets treated differently: German Heu with English hay, Feuer with fire, Freund with friend,neu with new, neun with nine.

Ceci n'est pas un seing.