It looks like you are well on your way to a nice machine.
About that mention of getting materials cut to size, I wasn’t thinking about the factories but rather your local lumber yard. Around here anyways most lumber yards have some sort of panel saw to cut sheet goods. Just a thought.
As for wood warping that can be a big issue if you live in an area where the humidity varies drastically. Sheet goods like plywood will minimize the distortion but even sheet goods can be impacted. Honestly I’m a big fan of steel in machine construction so I’m on your side there. Generally though we are talking about steel with larger cross sections. Even with that consideration it looks like your current design is closer to workable.
I need to add that die grinders or more specifically Dremel like tools, don’t last long on CNC machines. That brand might be better but I really don’t believe it is that much better. The grinder will get you started but expect a need to upgrade rather soon afterward.