Firstly, allow me to congratulate you on your purchase! These little gems are getting quite difficult to locate now, so this is certainly a nice find indeed!
I must confess that I have never experienced any difficulty in using the three-pole system to erect my Lyster Bag at events, but the poles which I use are in fact about 9'. Here's an illustration taken at a re-enactment showing the Lyster Bag with the poles:
I have also seen contemporary photographs showing these items having been suspended from three folding aluminum Litters. Unfortunately, I can only locate a partial view of this at the moment, but I will try to find a more complete photograph showing this:
Whilst researching this topic, I did come across this early war photograph, taken perhaps in the ZI, which shows the Lyster Bag having been suspended from three poles. As far as I can tell, there is no lashing applied to the top:
I hope these images will be of some use, and that you will be able to find some way of displaying your new gem!