Sort values and remove "0" with formula

Im trying to sort values using a formula.. I started with great confidence but ended up with a headache :)

If A1 = 0, i want the value from the next cell on the same row, less or greater than 0 to show up, and so on. Row by row. Excluding all 0 values and sorting the values less or greater than 0 from first cell on the left.

Is this even possible by only using formulas? I have tried different solutions with IF, INDEX, SORT, FILTER .. but im getting nowhere close to what im trying to do.

First image showing the start values:

And this is what im trying to accomplish using only formulas:

Thankful for all help I can get!

Best regards Jack

Here is one way to accomplish the desired output using one single dynamic array formula:

• Formula used in cell F1

=LET(
     a, A1:D4, 
     IFNA(DROP(REDUCE(0,SEQUENCE(ROWS(a)),LAMBDA(x,y, 
     VSTACK(x,SORT(TOROW(INDEX(a,y,)/(INDEX(a,y,)<>0),2))))),1),""))

• Or, If you want to fill down for each row then:

=LET(a, A1:D1, SORT(TOROW(a/(a<>0),2)))

• Or with using FILTER() function:

=LET(a, A1:D1, SORT(FILTER(a,a<>0,"")))

Or, this way as well:

=LET(
     a, A1:D4,
     b, SEQUENCE(ROWS(a)),
     IFNA(DROP(REDUCE(0,b,LAMBDA(x,y,
     LET(z, INDEX(a,y,), VSTACK(x,
     SORT(FILTER(z,z<>0)))))),1),""))