Here are the records if you allow consecutive positions in the line-up - entries which aren't just duplicated of the previous list are in bold.
Most runs as an opener:
839: Mark Taylor, Aus v Eng 1989
774: Sunil Gavaskar, Ind v WI 1970-1
766: Alastair Cook, Eng v Aus 2010-1
Batting at 2 or 3 is the same list as "batting at 3"
Batting at 3 or 4:
974: Don Bradman, Aus v Eng 1930
905: Wally Hammond, Eng v Aus 1928-9
834: Neil Harvey, Aus v SA 1952-3
These, plus Taylor, are the top 4 series for players at any position.
Batting at 4 or 5:
769: Steve Smith, Aus v Ind, 2014-5
753: Denis Compton, Eng v SA 1947
716: Everton Weekes, WI v Ind 1952-3
Batting at 5 or 6:
722: Gary Sobers, WI v Eng 1966
626: Michael Clarke, Aus v Ind 2011-2
623: Doug Walters, Aus v WI 1968-9
Batting at 6 or 7:
722: Gary Sobers, WI v Eng 1966
606: Denis Lindsay, SA v Aus 1966-7
562: Shiv Chanderpaul, WI v Ind 2002
Batting at 7 or 8 is the same list as "batting at 7"
Batting at 8 or 9:
315: Harbhajan Singh, Ind v NZ 2010-1
302: Shaun Pollock, SA v WI, 2000-1
293: Moeen Ali, Eng v Aus, 2005
Batting at 9 or 10:
291: Bert Oldfield, Aus v Eng 1924-5
250: Stuart Broad, Eng v Pak, 2010
249: Graeme Swann, Eng v Aus, 2009
Batting at 10 or 11 is the same list as "batting at 10".
If you allow longer runs of batting positions I think the only new instances are:
Batting at 8-10:
300: Sammy Carter, Aus v Eng 1907-8
Batting at 4-7:
779: Everton Weekes, WI v Ind 1948-9
You could consider non-consecutive batting positions, but I don't really feel like checking all 1992 options. :-)
