I would see how much a Lhr hel sin return in D class on AY that would get you the amount of points you need, getting a RTW is pointless for that amount of points you need. Unless you were trying for GGL.
Hel-Sin return is going to het you 5500+ miles not sure about the LHR HEL bit but I pretty convinced you will be a few points over 20000 after, given your time restraints you could do it over 3 day weekend.