What you seem to essentially be doing right now is starting with a negative for your first movement, which means that technically, your first lift is not a valid dead-lift, but something closer to a Romanian Dead-Lift or stiff-legged dead-lift, starting at the waist and going down, before being pulled up (although those are more straight-legged exercises than the traditional dead-lift).
One way to look at it is that, if you're always lifting the weight back up to waist height at the end to rack it, you're essentially doing the same movement, but in a different order. Instead of lifting up, and then lowering the weight, you're lowering it and then lifting it. It's essentially the same exercise. The only real difference I'd see is a slight one of safety for the first and last step. If you haven't gauged your weight properly, it may be slightly safer to be lifting the weight rather than lowering it, since if it's too heavy, you're more likely to just not get it off the ground versus having to bail or strain to lower the bar to the ground. I think that's a very minor risk, though, since presumably you get a good feel for it as you unrack it to lower it. Secondly, the negative movement of lowering a weight tends to be a bit easier than lifting it, so that last rep is slightly more difficult because you're putting it at the end rather than ending with a negative of lowering the weight. That said, the argument could be made that you're just making things a little bit harder at the end, which may be beneficial by pushing yourself just a bit further.
TL; DR I don't think your variation is going to have a major impact on your exercise. The difference is too minor.