We had ours delivered from Lake Erie to RI, via the canal. Took 13 days, daylight only, and that was pretty good. 2 days were west of Buffalo. Depending one where you start in LIS, that could be a day or two west of RI. So, 9 to 10 days is probably realistic from LIS to Buffalo.
The only hassle is having your mast dropped at the Hudson and restepped at Lake Erie. That can be time consuming and you have to figure out if you'll rig something to carry it on the deck or have it trucked across NY.
The canal can close temporarily, if a huge flooding storm comes through. It happens, so you can find yourself delayed. Half way down the canal is Lake Onieda. I can't say for sure, but would think there are marinas you could leave her in and return. Google the canal, there are a ton of cruising resources.
Finally, a boat that size may require its keel dropped to ship,over the ground. If so, it's just not worth it. On her own bottom is always better, whenever possible. Your $6k quote sounds pretty light, even just for the trucking. You must use someone highly experienced in hauling sailboats, not just someone quoting a generic per mile rate. Height, weight, length, etc typically drive premium permit costs and even escort vehicles, depending on the state being crossed. Add to that the cost to remove everything from the deck, including lifelines and stanchions, and reinstall.