There is a proposition that Alperton to Mornington Crescent can be achieved in four moves. However proof has not been accepted for the existance of this number.
I've had a cursory look at this and have found one flawed real-world solution and one ideal-world solution that only works in complex MC phase space. The Real solution is Alperton->Acton Town->Aldgate East->Moorgate->Mornington Crescent. The Imaginary solution is Alperton->Aldgate->Moorgate->Mornington Cresent. Unfortunately this is an odd-even move movement mapping which it is trivial to prove is irreconcilable. So you can cross that solution of your list as well. But this is only a first-pass approximation. It may be possible to use a one-move Expansion on the Imaginary at thereby unite the two. The trick, of course, is to do this without forcing a Real/Complex bifurcation.
OTOH, if you can acheive it /with/ an Re/Im bifurcation, then it's been proved that a true real-only analogue move to the bifurcated move does exist - if only it can be found. Which is the most tantalising thing about this puzzle. Theorists are almost certain it /can/ be solved rigorously, but no-one has ever been able to prove it.
Just a thought, but running with Kilydd's L~ton hypothesis and selecting Loughton over Leyton due to its greater magnetic selectivity quotient, how about stringing and ghost/live bifurcation on (move=2), possibly involving a recent ghost like Aldwych, or maybe Epping. The live side of course would have to be very lively indeed - maybe Baker Street or Bank. The dead:live dichotomy would perhaps then allow a move to a vortex station such as Sloane Square (Dollis Hill being unusable for obvious reasons). This might then lead to (move=3) being a Magenta station, though not if Baker Street had been used in (m=1) of course, it being a Magenta itself. What d'you reckon ?