The reason the oil companies started ULSD deliveries sooner than mandated was exactly your situation. They never completely drain their fuel storage tanks. By pumping out 80 to 90 percent of the fuel, then filling with ULSD, after 2 or 3 fillings the level of sulfur meets the federally mandated minimums. As I recall the actual sulfer content at the refinery is about half of the mandate number. The residual old diesel raise the "at the pump" sulfur level.
83 C10 Suburban, Silverado, 6.2, 700R4, 3.73, 31-10.50R15
82 C30 Crew Cab dually, 6.2, Banks, Th400, 4.10, Gear Vendors, 235-85R16
83 C20 Suburban, Sierra Classic, 6.2, 700R4, 4.10, custom paint, 285-50R20
95 Yukon, 6.5, 4L80E, 3.42, 265-50R20
73 GMC Astro 95, 8V71, 10 speed Roadranger, 110" WB, 6 each 11R24.5