Peter Elliot at Bislett in 1990 must surely have been the last non-African male to make a serious attempt on a senior world record?
I can't think of any other, and the EPO Africans soon put the records out of sight after this.
Peter Elliott's run at the Bislett Games in 1990 was touted as a serious attempt on Cram's Mile WR (certainly if you listen to the commentary by David Coleman (can't find that YT vid)). Elliott was in fine form and had run a1:42 800m very early in the season after looking superb in winning the 1500m at the Commonwealths. Unfortunately, I think he suffered an injury in the lead up to this race which also cost him the European 1500m title that summer. In the end, he was beaten by the American Joe Falcon, who I don't think ever really followed up this fine run with anything comparable in his career.
Who would have thought at the time this might be the last ever attempt by a non-African male on a middle-distance record, just half-a-decade after Coe, Ovett, and Cram were smashing WRs every other week?