Hmm yes, somebody's had a really good go at cooking that!
It looks as if someone put a lot of volts on it with a shorted output (or overloaded it in 'resistance box' mode) with the other decades set to zero.
I'm just wondering, did the 1k resistors drift high or low (probably low I guess). There's just the off-chance that if high, you could trim them down to correct value by adding high value resistors in parallel without too much degredation. It would obviously depend what input voltage you're planning to use it on (max spec is 250V) but if the input terminals still read 10k then I'd be tempted to start at 1V and then, cautiously, 10V, giving a 1mV resolution divider.
Your repair plan looks good, as it is a Rayleigh divider, the 1k resistors need to exactly match the total resistance of the next decade (in combination with the successive decades). That is hopefully the same value as the un-burned resistor (the last one looks ok).
Yes, I would still go for 4-wire measurement at 1k.
It's sad but I think still well worth the effort of restoration. I would send your photos to the seller as it probably doesn't count as 'OK condition'.