I'm no expert, and I'm not familiar with the Burlington and Grand Isle breakwaters either... but for whatever its worth, I can offer some advice on fall tactics for lakers
You're asking about using a kayak, and the Adirondack rowboat I sometimes use is comparable in terms of ability to get to the fish. Usually once the water cools below the mid-50's F (its been warm / late this year), trolling has worked well for catching lots of smallish lakers not far from shore. Rowing around 2.5 mph (by GPS) in around 40 FOW and parallel to shore around Converse Bay, Split Rock, and Whallons, etc. usually catches a few lakers this time of year. I use lead-core line, and between 2 and 5 colors of lead usually does the trick in mid October - mid November. Spoons like Honeybees #1s, Crazy Ivans, and Speedy Shiners are usually good.
Cold water safety is important if you're in a kayak, rowboat, etc. - I always have a handheld marine radio, stay near shore/other boats, and wear a wetsuit once it gets cold.
good luck, hope to see some photos of fish !
I do not exaggerate when I talk about fishing - I underestimate, like I say "just one more cast honey, then I'll come home" !
Keep Calm and... Fish On !