What value of resistor would I need? Any other methods?

Might be approximately calculated, but not practical because the resistor will hav to dissipate high power

It may be possible to use some choke (low voltage HPS ballast) in place of the resistor though. But what is the 400W ballast ? Does it have a capacitor ?

1.  Reaisustor of this size and valuev would be large and impractical as it would talke very high wattage such
A heating element cooktop from a stove. For current and voltsge droo.

2.  Using 4 x  100 watt HPS chokes in seriess
Will give 55 volt drop

3.  using multitap 1 Kw ballast as a auto transformer
With bo lamps connected  in  the output
Of 1 kw of ballast

The only way how that may really reliably work is to use another ballast as a transformer and feed the 208V ballast by really the 208V.

Any other option strongly depend on the exact architecture and properties of the exact ballast in use.
And it will definitely alter the ballast characteristic, which may make the lamp less stable to operate (more tendency to cycling,...).