To "First World Problems" ... for enough people for it to matter, this isn't a first world problem any more than coding is a first world job (and these days it isn't). As someone with hereditary back issues since my teens that, after 25 years of pain and bad surgeries with severe complications, I am now on disability. I wouldn't have made it 25 years without an extreme ergonomic solution that I paid for out-of-pocket because until recently employers didn't recognize that even "ergo chairs" aren't enough.
For the original question ... you're probably not as bad off as I was. But if you're getting close you have a few solutions depending on how much you can spend (or get expensed). If you're not looking for this level of solution, hopefully the article attracted someone who did.
* Not a recliner, but for helping your back similar to how an exercise ball does but with more support for long coding, I have used a "SwingSeat" at my desk for a decade or more (http://www.swingseat.com/). This was good enough to get me by until the last round of surgery (which was actually a success) made it too hard to sit upright all day.
* A "Zero G" chair, like the ones by Human Touch (I use a Human Touch Perfect Chair), a bit pricey but not awful. Combined with a laptop table that can raise and angle the laptop you can actually do the vast majority of your work from a completely reclined position.
* For a desk, rather than reclining all the time, I assembled a custom desk from Anthro using their Console line that has a tray that can raise and pivot from sitting to reclining (which actually needs to be raised higher than sitting) to standing (great for those of you who don't have partial leg paralysis, good for me on rare occasions). The desk is HUGE but dang, it does everything. It is the Console with full pole extensions bringing it to almost 6' with monitors on a shelf 8" higher than the shelf that hosts the keyboard tray. Which means the monitors can raise up to standing position as well. I can, if I use a trackpad to avoid mouse problems, use this in combination with the Perfect Chair as a rigged solution similar to the next one.
* I couldn't afford this, or at least I could have before I needed it, but can't now. But if you can, the desks from ErgoQuest are perfect. And some of them are inexpensive enough to be not tooooo awful on the budget (if I had the money I spent on the SwingSeat, Anthro Console and Perfect Chair I could afford an ErgoQuest). You can -sometimes- find these on Ebay but not usually from someone willing to ship and often not for significantly less than having the right one built to your specs.
I sympathize with you. But different folks need differing solutions. I used the Staples recliners, and tilted them to different degrees, adjusted arm heights, changed heights, and even tried ergonomic chairs as prescribed by Chiropractors. I bought what was defined as a programmer's chair.
Still, I had cramps in the legs, burning sensations on my hips, and general back fatigue.
In the end, the $7.00 flat resin chair from the hardware store was the best solution. I bought a cushion for it, and it was the best investment I made. There are no wheels, and there is no height adjustment, just a cushion. I have no more backpain, no carpal tunnel pain for my arms and I am without the back issues.
My three other fancy chairs are now collecting dust.