Paralleling contacts is NOT a good idea. The picoblade connectors are for thin wire, that for sure. To thin for my tastes. Both JST and Molex has connectors designed for LED's. Have you looked into them.
I think it would be appropriate to ask Molex or JST for a suggestion,
However, it might be appropriate to ask the interconnection company for if there is a chance that you might use them. Be prepared to be able to answer their questions: Volume, frequency, cost, MOQ etc.
So, why not: Hi, I just learned or your company. We are having a bit of a problem finding a suitable connector for: . We're looking at the following volumes and schedules.
Currently we are doing this (_,,,) and it isn't working out. What might you be able to offer?