why doesn't the %3.5f example print 877.99999?

Because %f rounds. (%d truncates.)

>perl -e "printf '%.16f', 8.78"
8.7799999999999994
>perl -e "printf '%.5f', 8.78"
8.78000

>perl -e "printf '%d', 4.7"
4
>perl -e "printf '%.0f', 4.7"
5

>perl -e "printf '%d', -4.7"
-4
>perl -e "printf '%.0f', -4.7"
-5
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And why does multiplying by 1000 make a difference for the %08d version?

If I were to guess, the floating point processor is forced to discard low-precision bits, and it rounds the result when it does so.