Oops, I must've skipped over this post. I'll answer it right now.
Try looking for a fan with regular prongs that you can plug into a wall outlet. I'll link one below that I have bought in the past. The fan is actually pretty strong. I'd set it on a timer so it isn't running constantly. I'd just set in on top of the cage (screen) and have the fan blowing air out--this will suck the air out of the cage when turned on and replace it with new air. The gaps that you mention are not sufficient for the chimney effect by itself, but the fan should do the trick. As long as your air doesn't get stagnant and your humidity levels are correct, you should be fine. Though I'll never stop recommending a cage with adequate ventilation. With adequate ventilation, you won't need a fan. Consider it. I'm nervous about a tank with little vetilation--and all your fears would be gone if you got a proper cage. Do you have plans for an upgrade cage? I would recommend you creating a new thread asking for experienced people who have done this, but then you would get flamed here on the forums--nobody recommends a tank with poor ventilation--I'm just trying to find a solution to your problem.
Hopefully, other people will weigh in. I'm nervous about the setup, but IMO and use of rationality, I think you should be fine. We have addressed the issues that lead to RI. If we account for this in the setup, like we have, everything should be good. If anyone on the forums disagrees, let me know and we can discuss it.
Fan:
https://www.amazon.com/gp/product/B009OXTWZI/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&psc=1
And for the escapees, have you tried cup feeding her instead of letting the bugs free roam? If you got dubia roaches and put them in a cup, they wouldn't be able to escape.
--Sorry again for missing this post the first time. Haha, I'm finally going to sleep!