OK small timeline. Wagner seems to make it like its post-Production of DUNE and at the time of its release. So we figure the CONAN III of his in one variant or another was probably floating around by the time CONAN II and Dune were hitting the theaters.
Stout's "Conan and the Eye of Death" is dated as being 1983(no known month that I know of). So these scripts were surely being produced at around the same time for a back to back sequel expected back then to hit the theater at around 1985 or '86(Sonja timeframe). Arnold also was wanting outve his 5 picture contract by this time and made "Raw Deal" as an end picture and just popping up as a favor for Dino for the Sonja picture.
Dune only made a little more than 2 million dollars over CTD, which production value was diminished in favor of DUNE's production. Both movies combined, it only made as much if not a some more than as CONAN THE BARBARIAN's domestic gross back in May 1982( $38 million),lol.