I have some suggestions for you existing shoe. I assume you have already tried butterfly lacing and thicker socks.
1. Make your own elastic laces out of 1/8 inch shock cord and fasten it with a cord lock. Then, use butterfly lacing on the top laces. You may have to punch out the eyelets slightly to get 1/8 inch shock cord through them. Commercial elastic laces are okay, but not as good as the thicker 1/8 inch shock cord. I've explained how to do this before on Letsrun so you should be able to find more detailed instructions. If not, post back and I'll repost it.
2. Punch a new set of eyelets about 3/4 inch behind the top set of eyelets. That is, closer to the heel of the shoe. Skip the original top set of eyelets and use this new set of eyelets for butterfly lacing. This should really snug the heel into the shoe and stop any slipping. Again, use 1/8" shock cord instead of regular laces, although you can try it to see if it works with regular laces first. (You could bruise the top of your foot where the laces cross doing this with regular laces.)
3. Cut a piece of crafts felt about 2" high and 7-8" long. Look inside your shoe for the heel collar material. About 3" from the heel on the inside of the shoe, you'll see where the heel collar material is sewn into the front material of the shoe. Just put the crafts felt into the shoe and curve it around the heel so it basically forms another layer of this heel collar material curving around the heel and going about 2-3" along the side of the heel. Carefully put on the shoe so as not to move the felt and then do a short test run. This will shove your foot forward in the shoe and make a snug fit in the heel. It should stop the slipping. It will also change the entire feel of the shoe... almost as if you made the shoe a half size smaller. If you're okay with this and it works, trim the felt to fit and then use spray glue to hold it in place.