Welcome to TVPaint Community forums !

When I surround a drawing using the Freehand Selection and then hit Shape: Transform Position, it pops my drawing to a different size and position on screen. Is there a way to make it so that the drawing stays in the same place until I use the bounding box to manipulate it?

you can (sort of) fix it but you have to add a Reset tot the keyboard short cut.
add Tools: position reset Position
and for future use you could also add:
Tools: position reset Scale
Tools: position reset Panning

to add multiple actions to a key hold CTRL while clicking Assign.

Note... for some reason you have to click the key twice, the first time it will let your selection do what was last done with the shape transform,
but after clicking again it will snap to reset and you can start a fresh transform.

Thank you so much, Peter!
I'll give that a shot.