CONCURRENT SELECT's SLOW .... LOCK IN SHARE MODE
INDEX(type, stamp) should speed up "Select 1" significantly, even without LOCK IN SHARE MODE.

(Please provide SHOW CREATE TABLE for further discussion.)

Edit

Even though you have type and stamp in indexes, having these two fields in this order will be optimal for "Select 1":  INDEX(type, stamp).  This is because the optimizer can drill into the BTree to the end of the "type='string'" values and find the MAX.  Instantly.  Only one rows is fetched.  And it is only fetched in the index.

With PRIMARY KEY(type, other stuff) it needs to scan 6M rows to find the answer.  COM_KEY is of no help (for this SELECT).

After this query is sped up, the other queries may be less of a problem.