Which Embera Community?
I believe there are several Embera communities (including but not limited to Embera Drua (Upper Chagres), Embera Puru and Arimae), and hence various different places one can be picked up along the Chagres on the way to the village. Hence this question is kind of on the broadish side according to TSE's regulations. Nevertheless I understand that finding information on the topic is quite challenging, and I assume that for the purpose of your question any information to privately reach any village will do. So here we go.
Visit Embera Drua
This webpage from Native Planet explains how to visit the Embera Drua village. It suggests contacting the village to arrange a private visit. More importantly, it mentions a rendez-vous point on the lake, which I assume is Lake Alajuela, at Puerto El Corotu. This might be the place you are looking for.
As it turns out, the Embera Drua community has it's own website, with information on how to visit, and detailed instructions on how to reach Puerto El Corotu. Quoting from the website (emphasis mine):
Driving Directions from Panama City
Take the Transístmica Highway to the community of Cabima. Or, to arrive quickly (and bypass city congestion), you can choose to take the Corredor Norte to the "Colon / Las Cumbres" exit, where you will end up again on the Transístmica.
Then, continue north toward Colon on the Transístmica Highway for 6.8 kilometers to La Cabima. There, you will see a Super 99 grocery store, Mr. Precio and a Pío-Pío restaurant in a small shopping center on the right.
Turn right after the shopping center and pedestrian bypass. Immediately after turning, follow the road as it curves slightly to the left.
Continue for 6.5 kilometers until you reach the Bayano Cement Factory (Cemento Bayano).
Turn left at the factory’s sign marked "Cemento Bayano.”
Continue on for 8 kilometers until you reach a green and yellow one-story building on your left. This is the Panama National Environmental Agency (ANAM) station in Chagres National Park.
Pull in and register as a park visitor and pay a small entrance fee ($1 per person for Panamanians, $3 for others).
Exiting the station, turn left back onto the road. Follow this road to the lake. This is the port of Corotú. Welcome!
You can park your car at the port securely. There is a police presence overseeing the port all day.
Moreover, the website mentions the possibility of helping you arrange transport to Puerto el Corotu. Below are the contact details:
Ivan- Marketing and Customer Relations (507) 6709-1233
Community telephone: (507) 333-2850 in Panama
Please remember that we only speak Spanish or our dialect, Embera. Ask for Johnson, Tourism Cooperative President, to make arrangements in English.
(We review our email every 2-3 days)
Visit us on Facebook:
Google Maps Meeting Point
Curiously enough, google maps has a pinpointed location called Embera Meeting Point which could also be interesting to you. It's difficult to say if this is Puerto El Corotu, or even if it is for charter boats alone, or which community will be picking you up here. Nevertheless it's still a valid clue in my opinion.