If you can get one cheaply enough an old line drier from early fly fishing days is a very useful tool for the job, and accomplishes the task far quicker than anything I've tried.
Some of the very early models in really good condition can be very expensive, but take a look on e-bay as there are usually a few available at reasonable prices.
As to backing, I have used soft twine wound onto the spool and then covered with tape. Alternatively, for some applications then use Baz's good advice.
Hope this helps.