Perhaps it would be useful to post some articles from newspapers other than the New York Times. The Times, then as now, gave its own slant to the news.
Here is the Richmond enquirer of Richmond, Virginia of June 1, 1860.
https://chroniclingamerica.loc.gov/lccn/sn84024735/1860-06-01/ed-1/seq-1/#date1=06%2F01%2F1860&index=3&rows=20&searchType=advanced&language=&sequence=0&words=Democrat+Democratic+Democrats+DEMOCRATS+Douglas+RICHMOND+Richmond&proxdistance=5&date2=06%2F01%2F1860&ortext=democrat+douglas+richmond&proxtext=&phrasetext=&andtext=&dateFilterType=range&page=1
Here is the June 1, 1860, Weekly Pioneer and Democrat of St. Paul, Minnesota Territory reporting Senator Douglas’s speech to the Senate May 15 & 16, 1860:
https://chroniclingamerica.loc.gov/lccn/sn83016751/1860-06-01/ed-1/seq-8/#date1=06%2F01%2F1860&index=12&rows=20&searchType=advanced&language=&sequence=0&words=DEMOCRAT+Democratic+Democrats+Douglas+DOUGLAS&proxdistance=5&date2=06%2F01%2F1860&ortext=democrat+douglas+richmond&proxtext=&phrasetext=&andtext=&dateFilterType=range&page=1
Here is the Clarksville Chronicle of Clarksville Tennessee which offers another insight into the politics of the day:
https://chroniclingamerica.loc.gov/lccn/sn88061076/1860-06-01/ed-1/seq-2/#date1=06%2F01%2F1860&sort=relevance&date2=06%2F01%2F1860&searchType=advanced&language=&sequence=0&index=1&words=democratic+democrats+Douglas+Richmond&proxdistance=5&rows=20&ortext=democrat+douglas+richmond&proxtext=&phrasetext=&andtext=&dateFilterType=range&page=2
The Jefferson Democrat of Chardon, Ohio. Here I discover that Lincoln apparently won the popular vote for Senator against Douglas in 1858, but it was the state legislature that officially decided who won (column 6). Never heard that about the 1858 Lincoln vs Douglas contest before:
https://chroniclingamerica.loc.gov/lccn/sn84028083/1860-06-01/ed-1/seq-1/#date1=06%2F01%2F1860&sort=relevance&date2=06%2F01%2F1860&searchType=advanced&language=&sequence=0&index=4&words=Democrat+Democratic+Democrats+DOUGLAS+Douglas+RICHMOND&proxdistance=5&rows=20&ortext=democrat+douglas+richmond&proxtext=&phrasetext=&andtext=&dateFilterType=range&page=1
Excellent. Thank you for sharing these resources. I think the defunct New York Tribune is also available in miniature pdf form somewhere on the internet. I have no plans to expand my posts beyond the Times, Harper’s Weekly and excerpts from various volumes. I have no more spare time. So posts like yours are invaluable.