I made this trip this week, and wanted to share updated information on the journey between Copan and Livingston. Detailed version first, then cost and time summary below.
In Copan, tourist agencies only offer direct shuttle to Rio Hondo, for a cost of $20pp. Rio Hondo is less than half of the way to Rio Barrios or Rio Dulce, so it seemed pricey. From there, you would get on a public bus and be on your own.
Instead, I took a public bus (15 person shuttle, really) to the border at 7:30am from the Copan center (ask anyone in town where they leave from). By 8:20, I had crossed the border, borded a public shuttle (again 15 person van that is just as good as the tourist ones) to Chiquimula. Arrived at Chiqui bus station at 10:15 and was bombarded by local guys trying to push us onto any bus to Rio Barrios. Asked a cop instead and he kindly walked us to the reliable company. Waited 15 minutes to leave, again on a 15 person shuttle. Shuttle left us at 2:30pm at Rio Barrios dock (my request), boarded boat to Livingston for 30 minute ride, arrived in Livingston 3:00pm.
All in all, public transportation took 7 hours and only 1 hour longer than tourist shuttle would have taken, at 1/10 the price. I had front row for all shuttles- they do crowd them sometimes with standers, but just get a good seat by a window and stay there! If none are available, wait 15 min for the next shuttle. At the border and in Chiqui, they leave as soon as full so it's fine to wait. Here's the breakdown:
Copan to border: 20Lempiras ($1USD) 30min
Border to Chiquimula: 20Q ($2.80) 2hours
Chiquimula to Rio Barrios: 45Q ($7.50) 4.5 hours
Rio Barrios to Livingston (boat): 50Q ($8.25) 30min
*we could have waited longer and gone with more people on a boat for 35Q instead.
Highly recommend doing this via public transport if you speak some spanish (Chiqui terminal is a bit crazy otherwise). I found my seat more comfortable than the tourist vans, and the guys took great care of our bags, even bringing them inside the van when it rained!! Not the tragic chicken bus experience I expected at all.