First of all: Thanks for providing the apk here - I'm very happy with it.

Is there any progress on getting the App into the Jolla Store? Will it take so long for future updates as well?

The beta of the new Signal Chrome App is now available. You can also compile it yourself (German Tutorial).
It seems like you have to scan a QR-Code from Signal-Desktop and have to open a link in the QR: tsdevice:/someRandomHash

Will that work with the Jolla-Version of Signal?

Edit: Nevermind. Checked with an Android Device: You just have to go to devices in the Signal-settings and scan the QR-Code directly from the app.

Greetings