Chosen Solution
After putting off the upgrade for about a year and a half, I finally swapped out the battery in my early 2011 MBP with new stock from iFixit. The initial result was good: 6,058mAh through the first 3 cycles, per Coconut Battery. I did notice that it was taking longer to charge the computer, but I attributed that to the new battery’s size - I was working with 3,528mAh (61% of original capacity) on 1,616 cycles before this new battery. Couple days later, and I noticed two things. One, my battery capacity has already dropped off to 5,252mAh (91% of factory capacity) after 5 cycles. Two, my computer had charged maybe 20% over the course of 4 hours while on power adapter. Coconut Battery reported it was charging with about 3.66 watts. I have noticed this issue from time to time. Do you guys think it’s the new battery? The power adapter and cord? Or perhaps the MagSafe power port? My power adapter and cord is not as aged; I had to buy a replacement about 4 years ago. The MagSafe port is showing its age somewhat; it definitely doesn’t look very clean. When I reset the connection, sometimes it’ll jump to a higher wattage for charging (like around 12 watts). One last time I noticed recently was that the LED would slowly dim out once in a while - weird! Answers greatly appreciated!!
Wound up taking my computer to the Apple Store since they had an opening. They will spend quite a bit of time giving you their disclaimer that they won’t do any repairs for you since you’ve installed 3rd party parts into the system - ignore this. The battery replacement is a ridiculously easy job, and you don’t want to be paying them to undo a couple screws anyway. Anyhow, they ran a test that confirmed the problem was with the battery. It took maybe five minutes, and the same test also verified that everything else was in good working order (logic board, MagSafe port, charging adapter, etc). I also wound up getting my replacement battery on warranty from iFixit later that day, and the early returns on this new battery are encouraging so far. Lastly, I want to add that I learned it’s supposed to take about 4 hours for your MBP to fully charge from empty. The first 0% to 80% is done via “fast charging”, and is supposed to take about 2 hours. The last 80% to 100% is done via “trickle charging”, and is supposed to take another 2 hours. The whole point of this trickle charging is to avoid damaging the battery with overcharge once it’s near capacity, and is a logical explanation why you’ll have much lower wattage when charging during those conditions. I’ve verified this with constant observation using CoconutBattery, and my MBP now takes 4 hours or less to charge. Hopefully this info helps everybody who came to this thread with a similar issue. Don’t assume it’s the logic board right away - that’s a PRICEY part, and a hard fix, if I’m not mistaken. The Apple Store won’t charge you anything to diagnose the problem, so take advantage of that if you can.
Review this Apple T/N Apple Portables: Troubleshooting MagSafe adapters see if your MagSafe adapter is the correct one and the connector interface is clean and in good working order. Update (03/05/2018) Sadly, it sounds like you have a charging logic issue within the system. Lets see if we can isolate the fault. Follow this IFIXIT guide MacBook Pro 13" Unibody Early 2011 Logic Board Replacement for the first four steps, once you disconnect the battery jump down to Step14 disconnecting the battery charge indicator ribbon cable place a piece of tape across the connect so the ribbon stays disconnected. See if that changed anything.
I’m having your same original problem. And I just bought MBP 13 in June - about 4 months ago. But I use excessively all day doing cloud computing database work, and evenings watching YouTube movies whatever. That battery is like 4 years old in battery years since it’s been working 16-20 hrs a day for 4 months. If there’s a chance this level of use will ruin my system beyond the battery - I better find out now b4 too late. THANKS this was very helpful. Heading to Apple store for a level 5 diagnostic. Lol #trekkie