I remember Neillsville from "The Rock" radio station. ;)
So, to answer the question, we need to know where the water is coming from. You mention that it's due to a high water table.
As such, I'd not ever finish the basement. It will always be one power outage or one clogged drain away from being ruined again.
It also means that your dehumidifier will never 'win'. Basements are moist by default simply due to cooler temps, but if you have constant hydrostatic pressure, it will always be an uphill battle.
Your (what I call) interior footer drain will certainly help, but you're at the mercy of the drains always remaining unclogged and the sump pump always having power. You'll also have to make sure it can handle excessive rain during those big midwestern downpours.
If it was merely an occasional rain/snow melt issue, I'd feel OK finishing the basement, but given the high water table, I'd consider rethinking doing a full finish project down there.
If your water problems are primarily at the footer, It may be OK. As that is exactly what the drain system is designed to handle. But if you have actual cracks in the walls and water is coming in there, I'd be definitely be hesitant.
One other note...a bit further west into MN, the clay soil we were on had a lot of radon. So you may want to get a radon test before thinking of finishing the space as well.
Oh, one last comment: note that the systems being proposed are in no way 'waterproofing' systems. They are water abatement systems--in that they are designed specifically to not be waterproof and actually allow the water to come in so it can be moved out. It's a nit-pick, for sure, but actual waterproofing is an entirely different discussion.
It was (and still is) common to float cement on top of the floor for installation of ceramic tile. It provides a level and firm substrate to which tile mortar (thin-set) will adhere. 1 1/2" seems a bit thick though, maybe there were irregularities with the floor which had to be compensated for. I try not to float so thick unless I have to, and now I use cementitious tile backer board when appropriate. Or sometimes I mortar the tile directly to a smooth firm plywood subfloor in new construction applications.
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What you're referring to as Linoleum is probably vinyl. At room temperature, it's fairly solid and the good stuff will bridge minor variations in the surface without it showing through. By minor, I mean shallow embossed texture in the surface of the layer below, or thin grout lines between tiles. Even at room temperature, heat ribbon is likely to eventually show through because the vinyl slowly conforms to the surface.
When you warm it, the vinyl softens and becomes flexible and stretchy. In fact, warming the vinyl is a trick for getting it to conform in a problem area during installation, or for getting vinyl planks to stay together when some irregularity underneath pushes them apart. If you lay heat ribbon directly under the vinyl rather than embedding it in a smooth surface, the vinyl will conform around it and the ribbon will show on the surface.
If you don't want to embed the heat ribbon in another layer, you may be able to accomplish the result with radiant heating film.
There are a number of versions. In general, it comes in rolls of fairly wide, thin, flat plastic film. Sandwiched inside the film is a resistive layer. You make the electrical connections at the wall and hide it with molding.
Doing this under the floor adds a lot of delay from the time you turn it on until the heat gets through the floor and starts warming the room. An alternative with much faster heating is to use the film on the ceiling and paint over it to hide it. The sensation of using it that way is a little like having a heat lamp in the ceiling; your head will feel a lot warmer than your feet.