I think you want "sutra" somewhere. Otherwise it's who's the most "runner-ish".

Also, is "e" the right connective here? why not use "ce"?

Agreed for {sutra}. I think {ce} would deserve another translation on its own to show two possible ways of forming sets. Would you want to add it?

Okay, I've added another translation. I'm still not sure about ".e" though. I have this suspicion that you need to use a JOI. I think the logical connectives work at a level above the non-logical ones. So "lu'i ko'a e ko'e broda" = "lu'i ko'a broda .i je lu'i ko'e broda", which is probably not intended.

You can check the parse tree from jboski or camxes:

[1(2[broda1 (predicate var 1??) :] (3lu'i the set composed of (4ko'a he/she/it .e and ko'e he/she/it)4)3)2 [is, does] «5broda predicate var 1??»5]1

You can see the x1 of broda is "the set made by {ko'a} and {ko'e}".

The same happens with {ce}:
{ko'a ce ko'e cu broda}:

[1(2[broda1 (predicate var 1??) :] (3ko'a he/she/it ce in a set with ko'e he/she/it)3)2 cu is/does «4broda predicate var 1??»4]1

Again, the x1 of broda is "{ko'a} in a set with {ko'e}".

Yours is simpler, however, and thus preferable.

The parser only gives you the parse tree, not the meaning. I know your sentence parses correctly, I'm just not sure it's semantically correct. I could easily be wrong though.