I fly fish in chest waders. They are great unless you slip and fall. Then they try to take you to the bottom. You will need a line connecting you to the TI, so they can recover your body.
(now I am not having a go at you but trying to dispel a myth) , I have heard this line before that, the waders sink you.
• However, if the waders themselves are not heavier than water, they do not sink;
• The water that fills them is not heavier than the water around you, it does not sink you; and
• if you are wearing buoyant clothing or a PDF, then the waders filling with water simply cannot take you to the bottom.
• Without the PDF
you could easily have air in the waders move up to the feet end and make your feet more buoyant than your head end and that would not be so good.
• So if you are properly kitted out, the worst that can happen, if the waders are loose and have a lot of space to fill with water, is that they fill up making them like a big water filled bag. This admittedly would make it really difficult to swim back to the river bank or to the AI if you went in.
So yes your idea of a tether strap to the Island is not a bad idea.
But if you have the top of the waders properly done up, wear a wader belt around the middle
to stop too much water going in and you wear an appropriate PDF
which you should do anyway if you are out on a kayak.
Then you simply cannot sink.
For fly fishing, there must be other alternatives to a bulky PDF that would still help prevent you from filling up and floating head down in the cold river.