I found some software for sale, but it didn't work well at all. I found another piece of software that would periodically check a certain email address and print out the emails, but it wanted to print them all, not what I wanted either. So, I've been annoyed and watching for a couple of years now. Then, when I was working in the desktop version of Evernote for Windows 3.5, I realized that I could highlight multiple notes and have them all print to the printer or with my PDF creator software, to a PDF file.
I primarily work in Evernote online, but the desktop software comes in handy to clip things in documents and other places on my hard drive, so I've had it installed for a while. I stumbled across the multiple print ability, and it solved all of my problems. You get a private email address to send notes into Evernote with email, and I use it a lot to forward important emails to save them as notes. But now it's a whole lot more valuable. To print multiple gmails is still not possible in Gmail itself. But, by forwarding the important transaction emails to Evernote, I can print multiple Gmail messages out of Evernote as notes. I even get the attachments.
By putting a contact into Gmail called "Evernote" with that email address, all I do is click on Forward and start typing "eve" into the To: box and the Evernote email address pops in, and I forward with one click. To further automate transaction emails, I build Gmail filters to automatically forward emails to and from my client. I merely do a search on the client's partial email address in Evernote, and every email related to the transaction comes up. I then just highlight them, and I get one large PDF file in chronological order.