You should be working in points not inches. Second, what is the size of your AE comp? I build huge artboards for dynamic text animations all the time and have no problems as long as nothing extends beyond the edges of the artboard. My usual procedure is to create an artboard that is 5 or 6 X the size of my comp, build the "at rest" elements in their finished position starting bottom left, import as a comp, then resize the comp by clicking on the bottom left corner in the Advanced comp settings before I start animating anything. I convert all layers to 3D, add a camera, fly it around the comp with a null and move to my at rest scenes, trim the layer in and out points, then animate the position of my layers mostly using animation presets that I have built. The size of the artboard depends not he number of at rest scenes. for example 9600 points X 6480 points will give me 30 at rest scenes which will cover a long paragraph of narration. That's about all I want to put in a single comp.
BTW, you should also be very careful to have snap to pixel turned on if you have any single point lines in your artwork. It's also imp;ornate to have even dimensions. There are lots of tricks to using AE and AI together. Your 277 inches artboard when converted to pixels (points) is 16,382 pixels which is a HUGE video project. I just tried a test file with an object in each corner of a 16,000 point X 16,000 point AI file imported as a comp and had problems because it looks like AE imports the comp as 14,400 X 14,400. If you reduce the size of your to those dimensions, select all your artwork and hold down the alt/option + shift key and scale to fit the artboard you should be ok. BTW, it only cuts off the top and right images because when AE imports an AI file the bottom left corner of the artboard is placed at the bottom left corner of the comp. Check your project panel and you should see something like this:
I have not researched the documentation to see if this is a known and published limitation. It's all vector art anyway so it should not change the quality of your project at all if you reduce the size of your artboard.
(EDIT) A search of the help files revealed there is no note on the limitation of the artboard size. The 14,400 maximum size is consistent in CS6 thru CC 2015