So, a simple solution to solve the great need of Rads and Basil recipes.
First, the Basil recipe solution. Simply give a chance for Basil to spawn in any normal arcade stage, like a scenario room.
However, I'm well aware that this would advocate players spamming the first level of each tier, and I'm also aware of how poorly OOO sees abuse. The solution is simple.
Make it so that Basil will only be able to spawn, after a player has reached the Crossroads.
Basically, you're only able to encounter a Basil scenario room on levels 5-7, 14-17, and 24-28.
Also, Basil will always spawn at the end of a boss level.
But here's the catch, Basil only appears in the Arcade. He will never spawn in missions. So yes, if you beat FSC via the KoA mission, you will NOT run into Basil.
Now on to the Radiants issue. The answer is simple, create a Crystal Depor. Now here's how it works.
At every town (Haven/Moorcraft/Emberlight) there will be a big fire crystal in somewhere. Interacting with the fire crystal will pop up a screen.
Basically, the Fire Crystal Depot (temp name: FCD) will GIVE you Fire Crystals for something very simple.
Minerals.
You know those thousands of blue/green/red/yellow (or really, any crystal that isn't used for your pet) you have? Now there's a place to spend them.
But here's the catch (because there will always be a catch), the Crystals that can be spent on the FCD rotates daily. Every 24 hours, the FCD will randomly choose to use any 2 out of the possible 5 minerals.
Since currently players have a huge stock of Minerals at the ready, here's how the exchange rate will probably go,
1 of any 2 mineral to create a 0* fire crystal
2 of any 2 mineral to create a 1* fire crystal
4 of any 2 mineral to create a 2* fire crystal
8 of any 2 mineral to create a 3* fire crystal
15 of any 2 mineral to create a 4* fire crystal
25 of any 2 mineral to create a 5* fire crystal
I know it may seem too easy for the players who've stocked up tons of minerals, but remember that the devs always have to think about the new players.
EDIT: There, how's that?
20 for 3 Rads would be pushing it a little. I mean, you already have 3 methods to collect Rads now, ALL of which can be done AT THE SAME TIME. (Boxes, depot, and this)
100 for a single 5*, thats way too low, even for massive stockpiles
20 for 3 5*s is reasonable, you know, because you need to WORK TO GET SAID STOCKPILE
really the way you have it is worse than the supply depot
edit: that is acceptable