Clay Davenport publishes all kinds of advanced stats for the majors and minor leagues so, for whatever it might be worth, I took a look at some of defensive runs above average he calculates. I have no idea what method he uses to get these numbers.
Here's the link: http://claydavenport.com/stats/webpages/2018/2018pageTORrealALL.shtml
The site is a nightmare to navigate. The defense numbers are on the far right of the table. I believe the format "13-3B -1 12-2B 2" translates into "13 games started at 3B, 1 run below average. 12 games started at 2B, 2 runs above average. There are tables for the different teams (MLB down to Bluefield).
Notable numbers:
Vlad Jr was +4 at both AA and AAA. For some reason I'm just a bit skeptical of him being a +8 defender at 3B but it's certainly encouraging to see positive numbers.
Alford +1
Jansen -5 (Buffalo)
Pompey -2 RF, -2 LF
Tellez -1
Roemon Fields +7 CF, +5 RF (I included him only because of the high numbers and proximity to MLB)
Biggio +6 2B, 0 3B
Pentecost +5 C
Harold Ramirez -5 RF, -1 LF
Bo Bichette -1 SS, -1 2B
Kevin Smith (Dunedin) +8 SS, +2 2B
Kevin Smith (Lansing) +3 SS, 0 3B
Warmoth +3 SS, +2 2B
Ryan Noda +1 1B, +2 LF
Chavez Young, +2 RF, +14 CF
Samad Taylor +7 2B
Otto Lopez -1 3B, +2 2B
Griffin Conine +12 RF
Cal Stevenson +10 LF, +3 CF
Jordan Groshans 0 SS, 0 3B (only 11 starts at Bluefield, though)
Note that I only included Kevin Smith and Vlad's numbers from different leagues. There were other guys who split time between leagues but I didn't bother adding them. There really wasn't much in the way of significant mid-season promotions outside of Smith and Vladdy
Cal Stevenson and Chavez Young might be more intriguing than we think. Kevin Smith top 60 prospect?
Again, I don't know what value these numbers have but they're fun to look at.