Thanks to everyone for the very helpful and informative replies.  I do have a couple of follow up questions:
Your best bet would be 11" x 11" x 11" boxes (or 12" x 12" x 12"), the
records packed vertically (standing on end) tightly within but without
bulging and then use crushed newspaper to pad, as you suggest.

Is there any particular reason that 11" x 11" x 11" would be better than 10"x10"x10"?  The 10" inch box would certainly make for a tighter fit.  Is the concern based on the fact that, with a 10" box, the edge of the records would be touching the interior walls on all 4 sides?  The 10" boxes are about 20 percent less expensive than the 11" boxes - but since my main concern is that the records arrive in good shape, that price difference is certainly not my deciding factor.

You can leave the 10" records in the albums, but I cut all the sleeves 
with an Xacto knife and tossed the cardboard outers and saved some 
space and

I am going to want to keep the storage albums as I have a feeling that I will have an easier time getting some of my money back by selling them than I will finding someone who wants the records that don't match my listening tastes.

What is the best way to pack the filled albums?  Yesterday, I experimented with a 12"x12"x12" box and found that 10 inch albums fit very nicely inside. Obviously, I would want to make sure that the top edge of the albums all face in the same direction and that the box is oriented so the records are vertical.  My concern is with the safety of records that might be in albums that may have only 1 or 2 out of 10 sleeves filled.  I have not seen the collection in person,  so I am not sure what percentage of such albums there may be.  When I look at empty or nearly empty albums, I notice that the ends of the covers come together at an angel.  Completely filled albums, on the other hand, form a perfect rectangle and the records appear to be flat against each other. If a partially filled album were packed between a bunch of other albums which were completely filled, would the records in that album be at extra risk - or is the spine of the album cover designed to prevent that from happening?  Is it recommended that, once in the box, the spine of the album covers all face in the same direction as they would if they were placed on a shelf?  Or is it better to alternate the direction of the spine on each album?  I have never really trusted albums so I rarely use them.

Thanks again for all the help.