I have a couple of bins that got modified years ago that are set up to drop the grain out the door - just has a slide on the door.  The grain vac has worked OK to just suck it form the opening but is slow.  I ended up getting some of the grain ports to mount in the bin wall.  I think they are made by Tought T down by someplace near Cooperstown.  Rott Keller in Fargo sells a different brand also.  They are not installed yet but looks like you could put a 10" auger with a safety cage into them.  They also have a cover that should seal up well enough if you have air tubes.

My Brandt 8" auger does fit through most holes but it is a tight fit.  I usually use my 7" Brandt auger which has more give.  My 8" Alloway Westgo has a larger cage than the Brandt.

One trick I started doing years ago was to wrap a truck mud flap around the auger as I was putting it in the bin.  Kept the grain from being pushed out with the flighting as I was winching the auger in.  I usually had a come - a - long to help pull the auger into the bin.  When the auger was in fast enough, I then took the mudflap off (which is just sitting by the bin opening even though the auger cage in now inside in the bin more).

I know what you are talking about and have tried different things on those old Montgomery Wards bins and others.  I do not like to use those old small bins without take outs but sometimes you do what you have to do.