Shards need increased chance to capture and master should be priced to make them monetarily bad (20 percent more not 1200) but timewise good.
5 selenvium per stage 3 run avg would feel better as right now getting MAYBE 1 per run is way too low especially when you need 30 for just an advanced harmonic stabiliser. As it is now that is probably 45 stage 3 runs.
I would like to see higher tier illuvials more often but have the autobattler mechanics add to catching. For instance catching an illuvial with more points left gives a slightly higher chance of a good stat illuvial (x% more per x points over a set amount). Let the rarity of illuvials be their stats and breeding not just finding them. This makes the overworld more fun as you see better illuvials more often and incentivizes more play/grinding/leveling/burning for the "perfect illuvial".
Currently running around for 45 minutes to find 12 encounters of tier 3 and 4 stage 1 illuvials gets old fast and the random rare illuvial doesn't make up for the rest. Adding more variety of stages and tiers of illuvials would make it much more interesting and adding a bonus for good positioning and play would make battles feel more meaningful.
To combat the increased number of illuvials in the game you could add a burn mechanic where you have to burn illuvials to create something similar to shard dust which is used to fuse illuvials. You would have to burn similar tier illuvials to fuse as dust in addition to the illuvials you are leveling. You could also add a leveling design where each level or every so many levels you can add points to the stat of your choice to an illuvial and when maxed you would have a near perfect stat illuvial. To get a perfect one you can spend fuel and roll for a chance at perfect/burn where the higher the level the higher the success rate. Therefore time with an illuvial can be traded for good stats. Breeding or a super lucky catch would be another way to get a perfect stat illuvial.