Is it possible for one runway to have a different TORA in each direction?
Yes.  If you look at the information for London Gatwick as an example, 08R has a TORA of 3159 meters, whereas 26L has a TORA of 3255 meters.

http://www.ead.eurocontrol.int/eadbasic/pamslight-7B4054FA19E6240FA6A62C9356F52804/7FE5QZZF3FXUS/EN/AIP/AD/EG_AD_2_EGKK_en_2018-12-06.pdf