Range condition isn't the issue.

Mem 128GB, Innodb buffer 96GB,

That really is the distilled schema and the explain looks like this:

id  select_type  table     partitions  type    possible_keys                   key             key_len  ref                 rows   filtered  Extra
1   SIMPLE       tbl                   ref     PRIMARY,MemberA_status          MemberA_status  5        const,const         36178  100.0     Using  temporary;Using  filesort
1   SIMPLE       tblDates              eq_ref  PRIMARY,tblID_type_createdDate  PRIMARY         5        mlenz.tbl.ID,const  1      100.0

for:

SELECT
    tbl.ID
    , tbl.MemberA
    , tbl.MemberB
    , tbl.status
    , tblDates.createdDate
FROM
    tbl
JOIN tblDate ON
    tblDates.tblID = tbl.ID
    AND tblDates.type = 'T5'
WHERE
    tbl.MemberA = 4312
    AND tbl.status = 'S4'
ORDER BY tblDates.createdDate