^Honestly, with a vehicle that sketchy in terms of cleanliness I'd run a high mileage like Max Life full synthetic or M1 High Mileague from walmart.
Maybe even sub out a quart for 1 Q of MMO and be sure to do the short intervals of 3-4k max until you get filters and/or UOA that show less insols as cleaning processes (heck, even fuel system cleaning as well!) are going to increase insols which tell you that cleaning is going on. You just don't want to extend intervals with higher insols. Oil filter can't keep up with that much active cleaning in terms of 1) optimal engine protection and 2) quality oil service life for extending during a cleaning intervals.
I have used a blend of 2 Quarts Rotella T6 5w-40 from Walmart before with 1 Q of Mobil1 0w-30 + the 1Q MMO method. It turned out to be a very stout 30-grade oil; much like high mileage or racing 30-grade oil such as Red Line in terms of viscosity.
That got a nice tick for insols in my case, which let me know it was doing some cleaning. I don't have enough cut open filters as evidence but it was a 20 year old vehicle at the time.
HDEO and high mileage oils may/may not clean 'better' than a standard synthetic of high quality, but it's my belief they tend to handle more in suspension such as a neglected app than synthetics designed for 'maintaining' a clean engine during extended intervals.
Just my .02
PS: Not sure if applicable but you could always run something like Red Line SI-1 in the fuel and maybe a combustion chamber cleaner like Amsoil's Power Foam as a piston/intake cleaning and soak before you change the oil. OFC, doing that would make any oil sample perhaps look worse but if you cut open a filter after that? \o/
The hype!!!