10.0.12534.56 is actually build 10052, which is smaller than build 10586. As to why the version number is numbered that way, only Microsoft knows.
You can go to build 10586 directly from Windows Phone 8.1 (even without performing a hard reset, although for technical preview builds performing a hard reset is usually preferred). I just did this with my sister's Lumia 535. However, make sure that you have a lot of time to spare. Depending on your device, this make take a lot of hours. My sister's Lumia 535 took around five hours, and for my Lumia 1020 it took around two hours.
All you have to do is Install the Windows Insider app again, tap on Get Preview Builds, select either Fast or Slow Ring (both have 10586 now), and once the configuration is done, simply check for updates in your phone settings.