Keith, the big rods would work slinging bait like a clump of sand eels out along the shore, probably couldn't toss an eel on it
but there are other things you can do. That 10 footer could be a good stick for lighter eels & plugs, swap out the 14# for 20# because you will not need the line capacity unless you're really lucky
and get a fifty. Is it a 2 piece rod? Glass or Graphite?
I use one of three rods on the cape fishing 75% eels for bass and 25% plugs - I'm not a Cape regular and only fish it a dozen or so times a year. This is what I use personally but I think it's fairly typical in what's used for medium weight plugs and eels:
9' 1089 graphite Sabre rated 1-6, best from 1.5 to 3.5, lots of backbone, fairly fast action rod - can horse a fish if needed but that's really not as important on the Cape...
9'1088 graphite Batson, rated 1-5, sweet from 1-3, decent backbone, also fairly fast action
10' XRA1205 Lamiglas, rated 2-6, sweet from 2-4 (I never fish heavier so it might be better to 6)
I usually use a Calcutta 400 or a ABU 6500CL/Mag Elite conventional reels with roughly 150 yards of 20 # Big Game Green when I fish that area
Hopefully that info will tell you where your rods rate against those typical rods used out here...