MySQL how to migrate to new server without data lost

You almost have your answer already:

1. Create the new structure in parallel
2. Start writing to both structures
3. Migrate old data to the new structure
4. Only write and read new structure
5. Delete old columns

As for step 3, use something like this (in one transaction):

Insert what is not there yet:

INSERT INTO new_tbl (old_id, data)
SELECT old_id, data
FROM   old_tbl
WHERE  NOT EXISTS (SELECT * FROM new_tbl WHERE new_tbl.old_id = old_tbl.old_id);

Update what has changed in the meantime:

UPDATE new_tbl
SET    data  = old.data
USING  old_tbl
WHERE  new_tbl.old_id = old_tbl.old_id
AND    new_tbl.data IS DISTINCT FROM old_tbl.data;

New data will not be touched, because it is identical in both places.

You can use CNAME in DNS. When you're done with GARDB1, rename it to something else (GARDB1_OLD). Create a CNAME in the DNS server called GARDB1 which should point to GARDB2008. It should solve your problem because GARDB1 will resolve to GARDB2008 now. Ideally what you need to have is a generic CNAME that you can just re-point to a new DB server each time you are migrating. Perhaps next time you plan to migrate, you can implement it. Or you could go with what @SeanGallardy suggested.