I say this owning and collecting older Colts (including the King Cobra):
Prices have softened considerably in the last 2-3 years. While the original King Cobras are beefy and hold up to a lot, their design did not produce the smoothest action or best trigger out there.
1986 - 1990 Colt had a huge strike going on. They brought in replacement workers to assemble everything. That is generally considered the time frame with the least quality in Colt revolvers. So please keep that in mind when dudes who are trying to get their hands on an older King Cobra search more for an Enhanced model made in the early or middle 90s (they came out in '86 IIRC).
I've seen ones like yours, without the factory box and paperwork sitting at $1K without bids on Gunbroker. If you have the factory box and paperwork, you can add 20-25%.
There are still a lot of guys who grabbed up a ton of these 5 years ago when they were $1500 -2K everywhere. They're trying to sell them now for what they have into them, and of course the guns are sitting there with no offers.
Dudes can buy a new Python for $1,300 - 1,400, and even the new ones have more desire among the 'new revolver owner crowd' than an original King Cobra... So I don't see a resurgence in the collectability of them. If a guy is going to only own a couple wheel guns, he'll definitely choose a new Python.
So if it were me, and I was trying to move mine: $800 - 1K without box, and $1K - $1,200 with.