I-66 extension proposal from West Virginia
April 1970 Congressional Hearing on the status of the Federal-aid highway program

"commencing on the Atlantic Coast in the Hampton Roads area going westward across Virginia to the vicinity of Lynchburg, Virginia, continuing west to serve Roanoke and then to a West Virginia corridor centered around Beckley to Welch as part of the Coalfields Expressway described in section 1069(v), then to Williamson sharing a common corridor with the 1-73/74 Corridor (referred to in item 12 of the table contained in subsection (f)), then to a Kentucky Corridor centered on the cities of Pikeville, Jenkins, Hazard, London, Somerset, Columbia, Bowling Green, Hopkinsville, Benton, and Paducah, into Illinois, and into Missouri and exiting western Missouri and moving westward across southern Kansas"

This new description suggested I-66 would traverse a large chunk of south central West Virginia.
Kentucky initiated plannig and design on its portions of I-66, which included the segment from the Pikeville KY area to US 52 east of Williamson. This culminated in the 2003 EIS which showed the preferred alternative for I-66 to enter West Virginia near Matewan and meet the King Coal Highway near Varney WV, which is a little east of WV 65 on the new US 52 alignment that has been completed.
Kentucky completed a feasibility study in 2005 that decided the I-66 concept across their state was not economically viable, which cancelled anything related to I-66 in West Virginia.
In theory no part of I-66 in the Transamerica Corridor is still alive, though the current version of the priority corridor designations in ISTEA 1991 does still define the Louie Nunn Pkwy specifically as I-66 (while redesignating other parts of the corridor as parts of I-69 and spurs).
Like I-73/74, it appears West Virginia was in no hurry to build anything other than expressways instead of interstate highways, as the 2003 EIS says the West Virginia side was being designed to an expressway standard. This means that I-66 may not have been signed in West Virginia anyway?
At no point does anything suggest this I-66 would connect with current I-66 from Washington DC to I-81 Strasburg VA well north of all this, nor have I seen anything that suggests Virginia was looking at any point to build an interstae that would connect Norfolk-Lynchburg-Roanoke into West Virginia.