Recently I came across Photopea. Runs in browser: NO INSTALL needed (there is even Chrome app to run locally without Internet access), it is FREE and you have the WARP functionality with a bunch of STYLES to choose from (arc, bulge, flag, shell, ...). Those are forms with handles for fine tuning. Since the option is a little bit hidden, I give you a quick guide:
1) All paths MUST be on one layer (take a closer look especially after importing SVG from AD - you should merge layers if necessary)
2) Select the layer with move tool (all paths are now inside bounding box)
3) Click on the square handle in the MIDDLE of the bounding box
4) Click the WARP button from the upper toolbar (second from top)
5) Select STYLE from the same upper toolbar and shape your paths
6) Save as SVG and import back into AD
Don't be afraid of the pixel-like strokes in Photopea - those are regular paths.
I have nothing in common with Photopea - just helping AD community with workarounds. On another hand AD staff should bring this basic vector tool asap since this workflow sucks.
Hope it helps.