Print Register

Well, the Print register option does exist, so I'm confused by your request — and, I think, sorry that Quicken Support couldn't answer such a straightforward question.  

You print a transaction report directly from the register view, not from Reports. In this case, set your register filter to Last Year, then do Edit > Select All (or Command-A) to highlight all the transactions. (Alternatively, you can leave the date filter set to All Transactions, and select all the transactions from last year by clicking on the first one, scrolling to the last one, and Shift-clicking on that one to highlight all the transactions from the period you want.)  Then, simply do Print (e.g. File > Print, or the traditional Command-P, or click the Print button in the bottom menu bar).  In the little pop-up dialog box, make sure it is set to "Format as: Transaction Detail"  and "Include: Selected transactions only". Click OK, Quicken generates a report of all the transactions showing all the columns visible in your register — including the Balance column.

Here's a screenshot of the top of a register report for one of my accounts, and you'll notice the Balance column is the second from the right.



The columns are in the same order as you have them on the screen, so if you wanted Check #, which I have on the right, to be on the left or int he middle, you can just drag the column headings left or right in any register to organize them the way you want. Depending how many fields you have visible, you may want to switch the report format to vertical (portrait) or horizontal (landscape) orientation so all the columns fit on page wide. 

This seems to address what you said you were looking for; if there's something I misunderstood, please post back.