Your best chance is to play the caro kann with 1..c6, which often gives similar piece placement in the form of Bf5/e6/c6/nf6/nbd7
That said, if you are looking to seriously improved, trying to get londonish positions every game is a bad idea as you do not expose yourself to a wide range of potentially instructive positions.
Hello. I'm 34 and I have been playing chess for six months. As white I have had the most success with the London System and it is the opening I am most comfortable playing. As black I like to play the London System With Colors Reversed whenever possible. Is there a way that I could transpose into the London System With Colors Reversed if my opponent opens with 1) e4?