All you gotta do is go around saying, “Ugh, pet food…again? Enough of this Pet food! I don’t want anymore Pet Food! So useless!” And then the First Law of RNG Gods will deliver to you all that you do not want.
This is true except for the part of there being RNG gods. It's minions that control the MA and spire chests. I put curses in chat for the Inno minions when they start shorting me on 5d buildings from the MA and DAs from the spire. That works. Believe me. I use 10 or more building every 2 weeks (zero cooldown so they work for 2 tourneys and spires). You have to speak in the language they are used to hearing from the upper Inno-ites who stomp on them. The minions laugh at you and give you what you don't want if you ask for it or say you hope to get them. No, a good old curse is what works.
Here's an example of one I adapted from Ivanova in Babylon 5:
"Pathetic Inno lackeys, give me DA's in the spire and 5 day buildings in the MA or I'll rip your heads off and use them as chamber pots."
I have an even stronger one derived from Jamie in Outlander, but every time I'm about to use it, they give me what I demand.
How do I know it works? Even using the 10+ every 2 weeks I have 41 in inventory at the moment (I count a DA as 2). It varies, but when it gets down to 30, it's time to curse them again. Within a week or so, I'm up to around 50. I also have 163 pet food which is beginning to get low. I had over 220 a while back. Soon it'll be talk to the minions about that.
A more 'normal way' to get what you want: Don't be crafting or needing to collect something from the slot that gives the desired item when it rolls to another set of recipes. All buildings are in the 1st slot. Pet food is in slot 5. Time instants are in the 4th slot. The only things I craft from the 2nd and 3rd slot are the ones that take 5k spell frags for either 8 CCs or 1 CC and lots of Vision Vapor, 40 I think. Somewhere there is a list of the type of items each slot provides. I always use time instants to make sure I don't zone out and miss the time it rolls over.
Still, the curse is best. Use it to demand the moonstone library. Make your own or adapt one from the net. There actually are pirate and Scottish curse generators out there. Swear words don't work. Imaginitive curses are what you want, ones they haven't seen before. Ones they fear.