A D-cell is definitely a good pick; usually the issue with them though are space constraints. I have only used the TPS Booster with a single LiSOCl2 D-cell so far, but it has been working great with one of my devices for the last 2 months now.
You can indeed put two C-cells in parallel and it will share the current between them, meaning they can support higher loads from your system.
A major warning I have to give here though is that you should never put these batteries in parallel with something that has a different chemistry, voltage rating and/or state of charge. LiSOCl2 are non-rechargeable,so you want to avoid them charging each other. The only safe way to do this is to put two identical brand-new cells together, and throw them out once you remove them.