I have been able to find the updates on the server manually. The link is
http://42.121.0.77/cms/firmware/Boyue-T62KD1/. The battery seems to be a lot better. I'll post back with updates once I've run through several full charge cycles.
Furthermore, some more information about the device (I may create a wiki entry if that is possible and if I have time):
Model: T62D-HD -- (this was confusing because I was finding a lot of stuff about the regular T62D and thought at first that that was my device)
The device seems to be the same hardware as the T63, C67ML Carta2, etc. I am not experienced enough with Rockchip devices to say anything more about this, but simply that they have similar specs.
I'll try to host some images of the ROM once I have a chance to dump them.