I would certainly try adding some RES. I hate seeing parasites on caught fish!
Most of the people on the forum use RES to eat the snails that are part of the parasite cycle.
I don't know about their effectiveness on eating mussels. I have one type of freshwater mussel with thin-wall shells that I think the RES could crunch up to a certain size. I also have one type of freshwater clam with a thicker shell. I suspect the RES can only consume these clams when they are relatively small.
I cannot see how adding RES would create an imbalance in your existing fish populations. They will occupy a slightly different niche than your BG.
If you do add some RES, you might not see them very often in your pond. Unless you very specifically fish for them, you may only be aware of their presence by a reduction in your parasitic grubs.
I actually think my raccoons are my biggest predator on mussels. I frequently see footprints into the shallow water and a pile of leftover shells. However, they don't appear to eat enough to seriously suppress the mussel population.
I believe there are also some chemical treatments for mussels. Does any water from a stream or another body of water reach your pond during big rain events that fill your pond? If so, then this may be a difficult battle for you to win. If you only need to fight the mussels in YOUR water, then you may have a chance.
We actually have several people in the forum with aquatic biology backgrounds. Hopefully, they will drop into your thread and provide some expert advice (rather than my amateur comments).
I do like that you have a 60 y.o. pond that does not have duckweed or vegetation problems. That is a good sign that your trapped nutrient load is growing very slowly.
If you have too much water due to your large watershed, can you build a few swales to divert some of the water around your pond? That would probably make it less turbid, and would exclude a little bit of the incoming nutrients. If you can't do that, can you install some groundcover strips to slow down the surface water flows and perhaps filter some of the silt?
Good luck on the improvements to your 5-acre pond. I hope it brings lots of enjoyment to you and all of the other owners!