[r-t] Stedman problem

[Philip Earis]

I have another Stedman composing problem (a shorter one this time).  Any 
answers gratefully received.

I want to get from rounds to the row 197E5264830T in as short a time as 
possible, with the additional constrain that the touch contains back rounds. 
I'm happy to start from any point in the six, though the change 197E5264830T 
should be at backstroke, ideally at the six end. I have a preference for the 
back rounds occuring at a plain six end, but I'm not overly fussy about 
this.

I can do this in 48 sixes as below (using a conventional start), but I 
suspect something shorter will be possible.

1.4s.5.7.8.11.12.13.14.16s.20s (24 sixes to bring up back rounds)
1.3.5s.7s.10.11.13.16.19.21s.22 (24 sixes to bring up end point)

Can anyone help?  As ever, there's a pint in it for the best solution.

Philip Saddlton did have a program on his website 
(http://myweb.tiscali.co.uk/saddleton/stedman/turn.htm) to find the shortest 
possible turning course between two rows which would have been relevant, but 
sadly the lnik appears to be broken.