Large Number of ALTER TABLE Statements
Realizing that this is a complete redesign of your intent but why not script out the change for each table?  Ie create a new table, copy the data over, re-create all indexes, security etc.

The easiest way to do this would be to use the designer, make your changes, don't hit save, but instead right click on the background of the designer and request "generate change script".  Copy that out and you can then make changes to it as needed.  That way you only have 15 scripts to run.

I did this recently for a particularly large table (~700gb), using the script to create the new table and using an SSIS package to copy the data.  Then I ran the remainder of the script to generate the indexes etc.  This can be surprisingly fast depending on your needs.

Now if you don't want to do it that way you do have a couple of other options.  

You could put GO statements and use PRINT to print a status between each ALTER.  Then when you run your script you can tell where it failed.  It will only roll back the last statement you ran and you can run from that point forward.

Last option I can think of is to remote to the server itself (not considered a best practice) and run the script there.  That way even if you lose your connection to the server the script will continue to run regardless.