First, my apologies.  I'm in Ohio and unfamiliar with Oregon laws/regulations.  Somehow, this system often refers pond/lake management questions to me even though I've specified that I'm only willing to answer in-state questions.  I definitely recommend you double check anything I offer with your local Extension office: https://extension.oregonstate.edu/clackamas.

I did quickly review Oregon law regarding fish species that might be available as biological control.  I don't believe it would be legal to stock any to the site you describe.  I thus won't name them.

It seems that Grass Carp are legal to stock to some Oregon waters.  Within my own state of Ohio, I do not recommend them for algae control.  They may eventually come to eat algae, but they don't really like it.  They will favor grazing on soft-stemmed, submerged vascular plants.  In doing so, at least in the short term, they often make algae problems worse by removing beneficial competition.  They may get around to eating algae but not until the stuff they actually like to eat is absolutely scarce.

You're thus left with a few options:

• 4–6 feet is relatively shallow.  I don't know if this is practical, don't know the nature or height of your dam.  If possible (and it may not be), consider additional dredging to put more of the site's substrate at depths that might be outside the photic zone.
• Tolerate a diversity of native aquatic plants to provide beneficial competition for nutrients, space, and light against algae.  This is not a quick fix and would likely take years to manifest in results.  Also, with a site as shallow as yours, and depending upon what resident stakeholders think of aquatic plants, any aquatic plant has some potential to come to excessive coverage and be considered a "weed" issue.
• If/As permitted by local regulations, apply an algaecide (please check with local experts).  Formulas of copper are standard for algae.  A few taxa are copper resistant and would need more elaborate mixes to control.  Use copper conservatively by applying to two criteria: (1) apply as early in the season as the target is present in some small concentration (that will limit its potential for exponential growth into the season, but will still almost certainly need some reapplication into the season) and (2) the effective temperature has been reached (for copper products, that will as the surface waters are moving to around 60°F).

I hope this helps.

Eugene