This is the order I have my starting adventures in that I had planned for my local group:

1. Escape from Mos Shuuta (Beginner's Box)
   
2. The Long Arm of the Hutt (Free PDF download)
   
3. Crate of Krayts (Beta Book)
   
4. Shadows of a Black Sun (FREE RPG Day)
   
5. Trouble Brewing (Edge of the Empire core book)
   
6. Debts To Pay (adventure in the GM kit)
   

We have a mix of characters from Edge of the Empire and Force & Destiny and I want to run a mix of adventures to cover every aspect of the Star Wars universe. We have played through the first 2 on this list so far. At what points would you all throw in some Age of Rebellion and Force & Destiny adventures into this mix and what adventures? Or would you play all these Edge of the Empire ones first before slotting in ones from the other games?

I don't think order matters this kind of role play will likely come across quite episodic (not necessarily a bad thing)

From here I'd certainly add in Lessons from the Past (F&D core) and Hidden Depths (F&D GM) both may need a little tweaking to make sure their are rewards for the edge characters.

However it's worth noting you may need to tweak the difficulties of all the later adventures as your group may start to out power them; this should just be a matter of adding some set back dice/ upgrading a few dice rolls and possibly throwing in some additional minions

I don't think I knew that the betas had different adventures, I will have to look again.

I am looking at some of the force-centered adventures, namely Mountaintop Rescue, Hidden Depths, and Lure of the Lost. I'm sure you would want to start with Mountaintop Rescue but in what order should I run the other two?

Also, would it make sense to slot in an Edge of the Empire or Age of Rebellion type mission in between any of these or do you suggest running them back to back to back?

i have yet to play Hidden Depths but from what I've read it revolves around obtaining Rubat crystals. So if your force sensitive PCs want lightsabers (Presuming they don't have one) I'd suggest doing that one. As for Mountaintop Rescue and Lure of the Lost, well the important thing is to do Mountaintop before Lure due to the big "quest" of Lure being a continuation of Mountaintop. Without giving away too much, in Lure you need to find 2 Holocrons to help gain full access to a temple. For my campaign it took quiet a while to track the Holocrons, thus giving time to do another quest for kyber crystals and screw around at Naboo.

i have yet to play Hidden Depths but from what I've read it revolves around obtaining Rubat crystals. So if your force sensitive PCs want lightsabers (Presuming they don't have one) I'd suggest doing that one. As for Mountaintop Rescue and Lure of the Lost, well the important thing is to do Mountaintop before Lure due to the big "quest" of Lure being a continuation of Mountaintop. Without giving away too much, in Lure you need to find 2 Holocrons to help gain full access to a temple. For my campaign it took quiet a while to track the Holocrons, thus giving time to do another quest for kyber crystals and screw around at Naboo.

So where would you slot in Hidden Depths then? Also, should I start with Mountaintop Rescue? My group has so far played through Escape From Mos Shuuta and The Long Arm of the Hutt.

I've run all the above, and did so in the following order;

Mountaintop Rescue (Introduction of the Temple) - Beginner's box

Lure of the Lost (Conclusion to the Temple quest) - Beginner's bonus adventure

Lessons from the Past (Gives a good setup for finding the planet in Hidden Depths & parts and pieces for sabers) - Core

Hidden Depths (Gives the crystals for your lightsabers) - GM's Kit

If you're working it into a EotE campaign, you can slot them in anywhere, as they are all good at providing their own hooks. I wouldn't worry about the encounter difficulty levels, but you'll definitely need to give the BBEG at the end of Lure of the Lost an adversary upgrade or two.