Something’s off in all this.
Why are you sending a flattened raster file as a PDF? A flattened file is a pretty straight-forward thing — it doesn’t need to be wrapped up in a PDF.
As for the size, you’re apparently compressing it while making the PDF to make it smaller than a plain, old flattened file. You could always compress it more, but lossy JPEG compression will begin to take a toll on the integrity of the image, which you likely don’t want. Squishing it down to a size suitable for email will introduce so many JPEG artifacts that I’d definitely not suggest it.
Why are you so concerned about the size? Is it just because you think you need to email it. If you’re working with a normal printer, they will almost certainly have an upload feature of some kind. Have you checked their website? Have you asked them how they’d like to receive the file? Have you considered just uploading the uncompressed file to Google Drive and sending the printer a link? There are lots of ways to get the file to the printer, but emailing a big file isn’t one of them.