Reducing Exact Cover to Subset Sum in practise!
The short answer is no :-)  

Why? ... Because SUBSET SUM is weakly NP-complete; you cannot avoid the exponential blowup of the numerical value of the arguments with respect to the input size of the original problem
(in other words the length of the binary representation of the $a_j$  is kept polynomial by the reduction but the values obviously are exponential)

If this was not the case you could use Dynamic Programming to solve an NP-complete problem in polynomial time.