I had this problem with the photo in navigator being different than the filmstrip and main window and getting stuck that way in Lightroom 2 I believe and the solution then was to turn off "show photos in navigator on mouse-over" and I haven't had the problem since. I think it is ANOTHER long term bug that has not and will not ever be fixed.
As far as the other problem, I just exported a file at 48" long edge at 500 ppi and got a file 16000 x 24000 pixels so it worked as expected.
Lr6 and OS X 10.10.3
I am having this same problem. I can set resolution in length and width mode, but if I do resize to "longest edge" it gives me this error all the time. Now, if I don't click in the box and change anything and set it to 300, then change to "longest edge" and change the longest edge measurement and am careful not to click in the resolution box, I can export at 300, but if I click in the resolution box it limits itself to 217.
According to previous threads, this is a known problem in LR6.
The workaround is to do the math yourself and specify the desired size in pixels instead of inches so that the PPI/DPI box is ignored.
The simplest solution is to use 'Width & Height and place the 'Long Edge' dimension into both. That seems to work without triggering the 217 ppi limit and It provides the exact same results as using 'Long Edge.'