One thought is that you could always just build a version of the view that filters out the current month by default or at the user's option (if you expose a quick filter control for them).
Depending on how often your data refreshes, you could use TODAY() in the calculated field you build to be used as a filter.
IF DATETRUNC('month',[Date Field]) = DATETRUNC('month',TODAY()) THEN 'Current Month'
ELSE 'Prior Months'
You can filter the view to include only 'Prior Months' and prevent it from affecting your trend.
Yeah, that's my plan if the trend line doesn't automatically account for partial months. My guess is no, but thought I would ask first.
Any other thoughts? Wonder if it's possible to create a calculated field that's weighted based on days of the month and use it instead?