I'm a DJ who recently produced a bootleg (2 tunes mashed together) and keep getting asked, "Where can I buy this?" How can get it listened to and maybe get some backing for licensing? This tune should be getting some airplay.
A bootleg is exactly what it says on the tin - an unauthorised record. Therefore you dont really have any rights here, no matter how good the resultant mix is.
You could put it out yourself unofficially, on a white label promo, and send a copy to the label that owns the originals. If it gains interest worthy of a full release, you could negotiate a deal from that position.
As to getting it listened to, it's a booty, get it to the shops!