I put a 20 seconds pause after the Update. Here is what it gives:

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Adding MyTable.FaxPhone-Temporary...
Updating MyTable.FaxPhone-Temporary...

(1838535 row(s) affected)
Waiting for 20 seconds...
Droping column MyTable.FaxPhone...
ALTER TABLE DROP COLUMN FaxPhone failed because one or more objects access this column.
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I have to say I am beginning to run out of solutions. I tried a lot of things and something is causing this behavior which I cannot explain.