$14-15K seems more likely. The 100-300/2.8 is ~50% more than the 300/2.8 (current street price, 35% more than the launch price). The 500/4 launched at $10,300 and is $9K today, by analogy to the the 300 that means the 200-500 lands at $14K. The EF 200-400 + 1.4x launched at $11,800.
When you say 'price hikes for the other Big Whites', what do you mean? The RF 400/2.8 and 600/4 are the exact same price as the EF MkIII versions (which makes sense since they're basically the same lens with a bolted-on adapter). The RF 800/5.6 launched at ~40% more than the EF 800/5.6, that's in line with the 100-300 vs 300/2.8 II, but the EF 800/5.6 is a really old lens that never got the MkII/MkIII improvements the EF Big Whites received.
I think your estimate of $20K is way too high. Not that $14-15K is a bargain...