This is a very interesting story! I'm not sure the names and dates tie up though. Alexander Lindsay, the 6th Earl of Balcarres did not become the 23rd Earl of Crawford until his son claimed the title (1848) long after his death (1825). It also doesn't mention the Earl, Alexander Lindsay (around 1813 the date of marriage) having a daughter called Elinor, but she may have been 'deleted' from the family, or may have been a niece or other relative. But overall, more is written and kept about the titled people and they're easier to trace.
http://en.wikipedia.org/wiki/Alexander_Lindsay,_6th_Earl_of_BalcarresThe History Shop in Wigan has been renamed and refurbished and is now:
Museum of Wigan life, Library Street, Wigan, WN1 1NU.
Tel: 01942 828128
E-mail: heritage[-- at --]wlct.org
They have different records at different venues, so it's worth emailing and asking them or Lancs Record Office if they hold the pedigree to the Earl of Balcarres or Earl of Crawford, or any letters (especially by his wife, Elizabeth) or a diary even. Another name to check would be George Lindsay 22nd Earl of Crawford, who must have been related to Alexander of Haigh Hall.
Looking at the marriage you mention 1813, it's worth getting the original record checked. But, if they eloped in secret she may have used a different name.
Good luck with this one, I think it's going to be a difficult trek.
Regards, Tipps
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