Hi Lcharlie,
You said that the faster you play, the more it happens, so I think you'll just have to go slower.
Here's a pretty great lesson on fine-tuning your strumming: https://www.guitartricks.com/lesson.php?input=18320&s_id=1408
And don't forget, Lisa also talks about strumming in Guitar Fundamentals 1 right here: https://www.guitartricks.com/lesson.php?input=23532&s_id=1914
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