Current booster with LM317 not working properly in LTspice simulation?
Loose the diodes on the output.  I can't even guess what you think they do for you.

Increase R1.  You want the transistor to kick in well below 1 A.  It probably won't do much useful until you get over 1 A thru R1 as it is.  I'd use at least 1 &Omega;.

Use a real power transistor.