I think you can get around it with two keys (not 100 percent sure though).

Clearly if you press a key tied to a single spell (say an instant cast with no cooldown) it will stop the castrandom from trying to cast the spell on cooldown.

Thus is seems to me that you could have short term (i.e. no cooldown) spells on one castrandom tied to one key and the long term castrandoms tied to another key. The short term castrandoms will always fire. The long term might hit one on cooldown but then you go back to the short term key, it fires then you can go back to the long term key ....

And you have a bit more flexibility this way you might have only 30 seconds spells on your long term cast random and need only hit it once every 30 seconds. So you spam the short term key then hit the long term key every 30 seconds or so.