Eric, your original post reminded me so much of a somewhat fond time, keeping my 2nd Pandora going for several months with such tricks.
I had the lid propped open just enough in my jacket pocket at all times, to get away with showing it off. Once to a game shop salesman after he demo'd the 3DS to me, to many "WTH is that!"..."It has 2 sticks..very cool"... "OMG its a full computer aswell!" comments.
I kept that up for a few months but was resorting to turning the unit upside down to open it and needing about 40 attempts to get a salvageable image to work with and keep propped open. Eventually she died completely and I then had simply amazing customer service from OPT to get me back up and running in time for a trip abroad that was pending.
Cant thank them enough for a machine you daren't part with, or for their customer service, which is without rival imhho.
Aw crap, I'm going on vacation the week after next, and if I RMA my Pandora next week, I won't get it back in time. So I have to make it last until the end of the week after the next.
Do as Eric advised and either keep it fully open (or at whatever angle currently keeps a picture intact) and then keep the lid propped open so it doesn't switch off, if you must close it for transport. Should keep it going beyond your trip with any luck.