With the following image, I have the text as a source, and want to deform it to the curve above, but when using the envelope distortion tool, the bottom half and sides get deformed too. I basically just want to deform the height so the baseline is unchanged, and stretched "vertically" to a line matching the curve. Have tried all sorts of things, but really struggling with this one.

I‘d try it in a horizontally orientation what inkscape is expecting in most cases for path effects and alike.

I tried that also, but adjusting the top changes the bottom, and so on, as below. I also couldn't see a way to adjust the bounding box, wondering if that's causing my issues?

Hmm, yeah, I'm looking at https://logosbynick.com/warp-objects-in-inkscape/ and it has different bounding boxes (that seem sized to the given paths) compared to what I'm getting. Tried quite a few of the different deformation options, and the bounding box is much, much bigger than my group of paths.

It looks your "cage" isn´t a closed path which is needed for an envelope deformation and it´s way too big.

Can you expand more on "cage" being a closed path? And how to fix?

That´s how it works here: rotate converted Text 90° clockwise and draw the envelope (cage) starting from bottom left corner: