Script font, semi-connected, informal

Remachine Script
Solved by: 

Hello fonty friends! I'm recreating some artwork provided by a client and identifying this font would be a great help. I think there are at least three - maybe four - different fonts here, but my main concern is the one for 'Debbie's". (I'm curious about "Hours" too, but I can do that in another post.)

I have checked Identifont, What the Font, and Bowfin Printworks (lovely site!). I also went through several other resources with no luck. A larger-resolution file is attached.

This is my first post but I'm looking forward to being a part of the community. Thank you in advance for your help!


Debbie's: Remachine Script by Måns Grebäck
on: may be Helvetica Neue Condensed
Hours: Southern Aire by Måns Grebäck
6 am to 3pm: Gillies Gothic or Airstream NF
Open 1 days A Week: handwritten ;)

Wow, thank you so much for the thorough analysis as well as the direct links! I see the handwritten one didn't fool you one bit. :D Thanks again!