There have been multiple tech
There have been multiple tech service bulletins for Forester and Outback tailgate modules draining batteries, so replacing your battery without addressing that will certainly get you in the same situation again. It should be no surprise that the batteries the manufacturer purchases are cost effective for them and provide marginal performance for you, so I would submit that getting the same battery is a waste of time and money.
I have both a Forester and Outback each with under 8,000 miles and both batteries died within weeks of each other. I chose to get NorthStar AGM batteries which are quite a bit more expensive than the original technology, but -- you get what you pay for. Even without any tailgate TSBs being addressed, I haven't had any battery issues.
Also, you may find that writing a nicely-worded letter to Subaru explaining your situation and suggesting it would be nice if they would help out with a partial reimbursement of your new battery costs, may just get you more than you would expect.