How did the 831mW on certification submission turn into 2,000mW on
manual and package?

JerC-

They lied!

My guess is that if challenged in court, they might claim that the higher power
was either

a) The result of using the car battery to power the radio instead of its
internal batteries,

or

b) The total power delivered by the batteries.

The case for (a) is based on power output being greatly affected by DC voltage.
A slight increase in voltage sometimes results in a higher percentage increase
in output power.

The case for (b) is based on FCC limits, which would likely be exceeded by (a).

I doubt that Walmart cares, but you could use this information to justify a
refund after their normal return period has expired.

73, Fred, K4DII