If you are worried about how long it takes for a bin cage just look for a really tall one so that you can prepare the lid when you have time and just cut a hole in the side for now. I have done that and was quite quick, plus Wiggles (who is also a Syrian) can't get out - I've tried with a treat
Obviously buying the Zoozone for her is the best choice as I'm sure you have heard all the glowing reccomendations about it...