I have the same exact card; no way to put it inside from the bottom, without open the case.
Once the case is open, I tried to push it in, but as you, I was worried; then I read that the cards needs a good push, since they fit snuggly on the connector; so I cleaned the connector and the pins on the board, to loose them up, then I just removed the keyboard and put the card from the top of the motherboard (I have the RF shield on it), then I put a dvd cover with a piece of paper in the space between the case and the board, and gently forced it in.
After few seconds it did a reassuring banging sound, and it was completely slipped on the connector.
I have no clue how you can do that from the trapdoor...the card would not even fit trough the trapdoor.
Also keep an eye on the card orientation...if it is not perfectly straight, it won't go in, and you may crack the connector (we are talking of ancient PCB, which were not that resistant to mechanical stress); just keep an eye when it goes flush with the case and then push the heck out of it
For the trapdoor you can just leave it open, but if you move the amiga the card does not have any support, so it will wiggle on the connector, and is not good. I found a small piece of plastic, that I've jammed between the trapdoor and the card itself, so it stays up without problems; doesn't move an inch!.
