Is it possible to rewrite this formula to not have to retype every xlookup?

Example data and intended result

For the data in C2:G12 I need to find the corresponding percentages of X,Y,Z for each of A:D and then add them all together for each year. Ideally I'd like to simplify this formula since in some cases I have up to 20 columns to retrieve the components for.

I've tried =BYCOL(D2:G2,LAMBDA(x, XLOOKUP(x,$I$2:$I$5,$J$2:$L$5,,0))) but I receive a CALC error and I'm really not experienced with using LAMBDA in excel in this way. Unfortunately I cannot use VBA for this particular problem.