There are loan names with non-stressed ё as well. For example, the surname of the mathematician Paul Erdős is spelled as Э́рдёш.
Regarding трёхсот: you may put secondary stress on the first syllable indeed, but I don't hear any difference between this word and the word двухсот, where the secondary stress doesn't appear, so it is not necessary.
Even more, you can construct longer words where secondary stress on ё can hardly apply: for example, трёхсо́тметро́вый.
You may want to look at the pronunciation of these words on forvo: