Personally I would say avoid the Q at all costs, VOY overused them like the Borg. Besides, according to Q the Q have always been, so it would make it kidna pointless.
As for a ship from the TNG/DS9/VOY period being flung forward in time, the PTB would have to have some serious balls to pull that off and do it right, rather than a weak show like VOY, where the ship was lost across the galaxy.
Also being trapped wouldn't be all that big a deal, slingshot around the nearest star and then they're home. Job done.
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)