"Anyway, they wouldn’t swap the battery unless I paid $1000 for a logic board replacement"
I reckon these are your choices:
1. Pay the $1,000 for a board replacement (I WOULD NOT DO THIS)
2. If the Mac still boots and runs with the existing battery, keep using it until it no longer boots.
3. Buy a 3rd-party battery and try replacing it yourself
4. If "none of the above" suit you, start shopping for a replacement. Be aware that new MacBook Pro's are due out within the next 4-8 weeks.
For the OP:
1. I agree. Don't do this as it is too expensive for the model of MBP.
2. Definitely viable and might be a good if you are holding out for a new model that will release sometime soon?
3. If you plan to use the MBP for a long time, then it might be worth it to replace the battery yourself (or have it replaced at a repair shop). Or you want to keep it as a backup machine.
Just watch out for some of those 3rd party batteries. I bought a 3rd party battery for a 2015 15" MBP and after I installed it the battery would work fine until it got to about 40% or so and then would suddenly drop down to like 5% or so and shut off soon after. Luckily I was able to return the battery for a refund.
After I found a genuine OEM battery and installed it in the MBP. It worked perfectly fine and I didn't have any problems with it.
4. If you want a new one and can hold out for awhile, then this might be a good strategy. The M1 models also perform well and are also worth looking into if you can find a good deal on one.