Q: I was just wondering whether a cleaner way of including set identifiers in a GDX file name has been invented..

Things are somewhat better:

set i /i1*i5/, c /c1*c3/;
parameter r_c(i,c);

file fhelp;
loop(i,
  r_c(i,c) = uniformInt(1,10);
  put_utility fhelp 'gdxout' / 'results_' i.tl:0 '.gdx';
  execute_unload;
);

The put_utility allows to construct a file name using the normal put features for the next gdx execution-time operation. An execute_unload without a file name specified will use the file name constructed this way. gdxin and execute_load work in a similar way.

Bruce McCarl has documented this feature in his McCarl GAMS Guide (in the IDE Help→Expanded GAMS Guide (McCarl). Search for put_utility and chose topic reading multiple GDX files.