Success. By backing up and hitting the brakes hard (repeatedly), you adjust them up to where they should be. That's my method after every brake job.
I do the same thing. I've replaced a couple of levers and adjuster cables over the years, but as long as I use a dab of copper paste on the star wheel threads I've never had any real issues with mine (except one adjuster cable that rusted completely through). I did reassemble them wrong once, the (mid shoe) cable guide popped out of the hole and that drum refused to adjust.
If you want to get them adjusted quick after a shoe change or service, apply the parking brake lever maybe three clicks, back up and brake moderately hard. A combination of the parking brake and stopping in reverse usually tightens the shoes up quick.
The main problem around here is nobody carries a complete brake rebuild kit. If you are lucky you get some useful stuff in a kit, but I most always end up ordering the pieces I really need one at a time.
Be sure and compare the length of your new adjuster cable with the old adjuster cable.
One thing I do that seems to really extend the life of all the barke pieces is I remove the drum and wash out all the dust, rust, slat and whatever at least once year. I use a bucket of hot suds, a bottle brush and catch pan. Then rinse with really hot water. Re grease the star wheel threads and the dab spots behind the shoes, check the wheel cylinder for seepage.
Another million dollar trick, dab a finger full of grease onto all of the wheel cylinder and other brake line connections. Wipe off last years grease and apply some new stuff yearly. You'll thank me when it comes time to replace brake lines. Ten minutes a year can save a lot of grief later on.