but the more correct way is to think of run-time and compile-time as a per-block thing.

Quite so, ++ (Per-statement, even, in the case of use.)

print("first");
BEGIN {
  delete $INC{'ModX.pm'};
  use lib '../';
  use ModX;
}
print("last");
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gets executed in the following order

use lib '../';           # Before "delete" because of "use"
use ModX;                # Before "delete" because of "use"
delete $INC{'ModX.pm'};  # Before "first" because of "BEGIN"
print("first");
print("last");
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In detail:

1. Compile print("first");.
2. Compile BEGIN { ... }.
   1. Compile delete $INC{'ModX.pm'};.
   2. Compile use lib '../';.
   3. Execute use lib '../';.
   4. Compile use ModX;.
   5. Execute use ModX;.
3. Execute BEGIN { ... }.
   1. Execute delete $INC{'ModX.pm'};.
4. Compile print("last");.
5. "Run phase" starts.
6. Execute print("first");.
7. Execute print("last");.