Yeah I am understanding you better now.. I hardly ever think of actual closets for growing anymore even though I did that for 2 years. :)
The tape flap job we use now is definitely not for stealthy applications, and is probably partially similar to what you initially tried with the ape-tape.
basically the idea is just adding some depth to the frame that the door will close on... but it's not really 100% unless you also have external flaps, to serve as a final barrier for the bit of light that seeps through the semi-flexible tape.
you'll need a stiff inner frame with weather stripping, like HISSH recommends, I think.
for the bottom of your door, i'd recommend just putting down a 1x2 or a similar barrier. just make sure ya don't trip headlong into your box and come down on the whole works :D