Any way to search across all log streams in a cloud watch log group?

What you need is the CloudWacth Log Insight.

It cost some money to do data scanning this way though

Once you click the log group in the CloudWatch Logs console, but before you click into an individual log stream, there is a button at the top right of the page labeled "Search Log Group". Click that, and it will take you to a page where you can search across all logs in the log group in a given time frame.