So, I did some experimenting with various non-magma methods suggested here. Some worked better than others.
Hatch-Drop:
It worked, okay, but I'm not really a fan. It tended to behave erratically, and took a lot of vertical space to make operate kinda well. And since it created a pillar of ice, mining out ice and then collapsing the pillar was necesarry to free up the room for more ice.
Another issue was that dropping a stack of ice cause a lot of collapse spam, and it tends to form little jagged pieces when doing more than a 1x1 tile. It also created a lot of floor pieces that fell by themselves without building up a full block properly.
Maybe it's possible to make this work, but it's just very inconsistent and requires a lot more construction and planning when mining out the resulting ice.
Linear Bridge / Tube Methos:
Worked pretty much as expected. Creates a line of ice that can be mined as long you want. More bridges for more ice. Even without pressure, it works pretty quick once you drop the bridge. You can actually create 3-4 lines of ice before you actually need to refill the chamber behind it.
Upwelling:
This turned out to work really well. By creating "donuts" of inside/aboveground tiles around a single inside/subteranean tile, you could force water up and create a donut of ice around a tile of liquid water. Better yet, you could do it up multiple z-levels. Once one floor was iced up, the water would move up to the next z-level and freeze that, until the system eventually reached pressure eqilibrium with the source. Once all the ice was cast, the pressure source was cut off to remove the system pressure. A quick flip of a pressure release valve in the bottom level would quickly drain down all the pressurized water. By queuing up 2 lever pulls associated with a flood-gate, the pressure could be quickly relieved while still keeping the bottom fill chamber relatively full, making re-filling the ice quite fast after the first fill.
The downside here is that it can take quite a while for the system to cast the ice, especially when starting dry.