An alternative to Tidal, there isn't.
Tidal, Beatsource, Beatport and Soundcloud all have something that distinguishes them from the others.
You either have to:
- Change your routine/session to accommodate the limitations.
- Use an different DJ software/older version of RB where track separation stil works with Tidal
- Get the actual songs, which in your case would be near impossible with requests as you don't know what they want before hand.