I’m thinking about the mirror and duct tape method, reflecting the tiny bit of mirror onto a well-cleaned dry-erase white board. I’ll be at work at the time, so...
I was going to say this "won't work", but it could be made to work. However, the requirements are severe. I should say requirement, I guess, because it is this, that the apparent size of the "tiny bit" at the distance of the projection, be much less than the apparent size of Venus. This is very nearly 1 minute of arc, or about 1/3500 radians. This means that with a 1 mm "bit" you would need a >> 3.5 meter projection distance to resolve Venus. You would need an elaborate "camera obscura" setup to have any hope of success.
Why not just use eyepiece projection with a small binocular?