Okay, let's try timeline for land/sea based version?
* About 1965, US Army would likely notice the AIM-9C being actively promoted by Lockheed. The year is important; around 1965, the US Army finally gave up on Mauler and cancelled the program. The MIM-72 Chaparral, instead of temporary measure, became the backbone of US Army air defense for foreseeable future;
* The idea of fitting AIM-9C on Chaparral - with a simple illumination radar, slaved to radar sight - came into mind of someone from Chaparral development team. While the Army in general weren't much interested, the Navy liked the concept enough, to propose cooperation in "head-on capable Chaparral" development;
* The first version of "Improved Chaparral" is tested somewhere around 1967-1968. It's basically the same Chaparral, with the addition of 16-kw pulse-doppler illumination radar (the doppler mode is for aiming, so the radar could discriminate ground clutter) and additional diesel generator on same M730 chassis. The radar is slaved to optical sight (a primitive scope is added to make it possible to use radar as sight also), and provided with large 1-meter dish to make beam as tight as possible;
* In general, the "Improved Chaparral" (I-Chap) is not very impressive. While system demonstrated head-on and cross-shot interception capability, the ground clutter made it impossible to use AIM-9C missiles against target lower than 500 meters overland (somewhat better over sea). Still, it worked better - and have radar for nighttime and poor visibility - so Army started to deploy I-Chap's in 1969, as OTL, instead of basic model;
* The Army is generally satisfied with Improved Chaparral system, and mainly worked on making it's radar capable of search & scan for target. The Navy, though, is not satisfied with Improved Sea Chaparral performance. While system is fit on several FRAM destroyers, Knox-class frigates and small ships (like landing ships and minesweepers), its poor low-altitude performance preclude from it's wider deployment;
* So in 1970s, the Navy started to seek for solution, and came with a two-beam version. Since the illumination radar of I-SeaChap is much simpler than aircraft radar, it didn't took much time to work out the solution;
* In 1972-1973, Navy and Army deploy a Super Chaparral system - with a two-beam illumination radar, and low-altitude AIM-9C-2 missile. It's now capable of intercepting targets as low as 150-200 meters overland, and 30-50 meters over sea. The Army version also have radar dish capable of separate search & scan mode, so the system could now be called fully all-weather;
* The low-altitude model is mainly used as additional armament for small ships, as plug-in armament for refitted ships and auxilarities. Iowa's would likely got them in addition to Vulcan cannons;
* In 1975, Navy, finally fed up with multiple confusing designations for the SARH Sidewinders (the official designation is AIM-9C, but the export designation is Radwinder, the surface-launched version is MIM/RIM-72C, and there are subtypes, like European version with AIM-9B motor!) officially pushed for AIM/MIM/RIM-82 Radwinder designation, re-using the old unused number;
* Due to large number of Radwinder missiles in service and continued production, the Navy in late 1970s decided to invest into developing a pulse-doppler version, hoping that progress in digital electronic would overcame technical limitations;
* In mid-1970s, USMC - who didn't like the idea of having separate MIM-72 Super Chaparral SAM and M163 Tracked Vulcan gun - put at effort to develope the "common turret", which combine the Vulcan gun mount and Super Chaparral radar and missile rails. The resulting system, called Vulparal (Vulcan-Chaparral) is deployed in limited numbers on LTV7 chassis as LTVAA system;
* In early 1980s, US Army, worried about the problems with "Sergeant York" SPAAG, desided to adapt USMC's Vulparal turret as "intermediate" solution. To solve the problem of basic Vulcan gun - which is now considered as not powerful enough - the 25-mm GAU-12/U Equalizer cannon is fitted instead;
* So when in 1984-1985 the numerous problems with "Sergeant York" became obvious to public, the Army just shrugged and pushed Vulparal as "proven solution that we, of course, always have as fallback option". Renamed "Vulpine" to sound better, the system is deployed on M2 Bradley chassis;
* In early 1980s, the Navy pulse-doppler Radwinder enter service also, finally solving the ground clutter problem completely;