How about a French press? No filters! Get the stainless steel model, though. We used to get the glass ones that were about $15 each but they broke at least once a year. The stainless steel was about $25-30 but will never break and it's easier to take on camping trips.
I've had one for many years and never managed to break it. Good idea, but the problem is that metal filtered coffee makes my wife's tummy hurt. Paper removes more oils and makes it taste "cleaner". Come to think of it, something else to add to my garage sale pile! I bet someone will give me $5 for it.
Why don't you use that one for your coffee? Then you don't need the expensive filters at all, and your wife can keep using the cheap ones.
I like light-roast single origin coffee and I'm geeky about it. The beans I prefer roasted with a week and commercially cost $15-$20/pound from my local 3rd wave coffee roaster. By roasting my own I get all that fanciness for $4-5/pound and 20 minutes of manual effort per week. Wife could care less, likes super dark roasted coffee and only grinds it once a week. I could just suck it up and drink the bad stuff but I'm willing to do the effort and it doesn't cost more so I feel justified in the luxury.
This pretty much illustrates my last point. Basically, you guys want very specific, high-end, artisinal luxuries, and now you're trying to justify it mentally by fretting over the cost of filters. If money is super tight (like if you are in a debt emergency, saving everything for a goal, struggling to make ends meet, etc.) then hyper-focusing on the cost of filters is basically rearranging deck chairs on the Titanic -- you need to be fighting your feeling of entitlement to that kind of luxury at all, not justifying extra spending because "it's so much cheaper than if I [got Starbucks every day, bought fancy beans, used XYZ process, etc.]."
OTOH, if money isn't that tight, then you can legitimately decide that this is a luxury that is worth it to you. But it seems to me that if that were really your situation, you'd have already paid the $26 for the better long-term investment, instead of fretting so much about handing over a single Andrew Jackson that's going to save you money in the long run.
I also want to note that it's really not about the coffee. It's about developing a mindset that avoids lifestyle creep. Like I said, your brain is really, really good at finding justifications for what you already want to do. So once you develop the habit of justifying artisinal coffee, then you start to apply those same skills to grocery shopping, or shopping/meal services (it saves so much of my time, and I'm better off spending that time at work bringing in a paycheck! Even when you never do actually spend that extra time earning more money to offset the extra costs), and then to furniture (gee, I'd really better buy the high-end coffee table, because it's so much better quality and will last forever -- even though the reality is that in 10 years it'll be outdated and you'll replace it anyway), etc. etc. etc. ad infinitum.
So if your goal is to be financially efficient, you need to start from the assumption that everything beyond the very basics is a luxury, and then do the math and decide what kind of luxury, and how much, you want, given the financial consequences. For example, say you don't like your apartment -- it's too small, and the neighborhood is crappy. You can spend another $100/mo. to move to a similar apartment in a better neighborhood, the same $100/mo. to move to a larger apartment in the same neighborhood, or $200/mo to move to a bigger apartment in the better neighborhood. The math says that you need $30K more in your 'stache to sustain an extra $100/mo. indefinitely, and $60K for $200/mo. You do the math on how much longer you need to work to save that much. They you figure out whether it's worth it. Maybe you decide another X months of work is worth it to get out of your neighborood, but 2X months isn't worth it for the larger space. Or maybe you're having a kid, and you need the space more, so you choose the bigger apartment in the same neighborhood. Or maybe you just say fuck it, I cannot live like this any more, and you decide you're willing to work 2X months for the bigger apartment in the nicer neighborhood. There's no right answer; the point is to do the math and understand what those choices are costing you in time.
Note that this works in reverse, too: if your new coffee maker is going to save you $15/yr, that's $375 less that you will need in your 'stache to FIRE. So: is saving that much money worth the amount of time and mental energy you're putting into the analysis? Or are you better off working to, say, cut $50/mo. off your insurance ($15K less required in your 'stache), or $100/mo off your grocery bill ($30K less)? The math tells you what your priorities should be.
The real benefit of this approach is that it makes you extremely conscious of how much luxury you already have built into your life, which makes you feel like you are surrounded by abundance, instead of so strapped you need to worry whether you can afford 5c coffee filters.
