Google sheet query to sum columns dynamically determined by a multi-choice selection from a dropdown

I have a table in a Google sheet that looks like this:

I use data validation to create a dropdown (from a range) and allowing multiple selections, such that I can choose any combination of quarters to sum together.

For example, to sum Q1, Q2, and Q4 I use this query

=query(A2:E4, "select Col1, Col" & XMATCH("2024Q1", A1:E1) & " + Col" & XMATCH("2024Q2", A1:E1) & " + Col" & XMATCH("2024Q4", A1:E1))

But I want to build this query dynamically from the values selected in the dropdown. I tried to split and then join the selected values, then use concatenate to add the pre and post joined parts, like:

=query(A2:E4, CONCATENATE("select Col1, Col", CHAR(34), " & XMATCH(", CHAR(34), JOIN(CHAR(34) & ", A1:E1) & " & CHAR(34) & " + Col" & CHAR(34) & " & XMATCH(" & CHAR(34), SPLIT(A8, ", ")), CHAR(34), ", A1:E1)"))

It looks like CONCATENATE is return a literal string, rather than a SELECT command. I've tried many different ways e.g., moving the select outside the concatenate, to no avail.

Any ideas? I figure there must be a much simpler way to do this.

SUM Columns dynamically

=LET(a, BYCOL(SPLIT(F1,", "),LAMBDA(x,FILTER(A2:E4,A1:E1=x))),
     b, A2:A4,
     c, HSTACK(b,a),
     d, BYROW(c,LAMBDA(x,sum(x))),
     HSTACK(b,d))

Sample Input

Sample Output

References:

BYCOL

LAMBDA

FILTER