I ended up with two pages of notes on house rules, and it became too much of a chore to remember all of these rule clarifications.
This may be an area where you have missed something, though it probably depends a bit on you and your group. From my standpoint, when those gaps in the rules arise, I just make a ruling as the DM and move on. Whatever makes sense to me, in that precise moment of the fiction, is how I rule. In this way, I keep Immersion high. From there, it’s not up to me to keep track. Instead, I offload that piece of record-keeping to the players to keep track. It’s their gear, after all. And if they crave that kind of consistency at times (“hey, you ruled this way last time”), then it’s their job to remind me, not mine to keep track of every ruling.
Otherwise, you end up with what you have experienced. Scouring the book for answers, then creating a secondary document you have to scour. Bah. My advice: move away from that sort of rule scouring that bogs you down and robs your table of immersion.
Finally, on this issue, the relic core might bestow indestructibility on an item, but the core itself is not indestructible. After so many hits, the core eventually will have to take damage, and then when the core is destroyed, the underlying piece of gear will lose its protected status. The same would be true for the release sling. Similarly, characters would be able to push gear for a benefit, and eventually they would have to to tap into these items, which will lead to their loss.
It also sounds like maybe you allowed combining of items, and I’m not sure I would have gone in that direction. ie, your relic core takes up a slot in your inventory; it confers a benefit on your armor, which also takes up a slot, for a total of two slots. The two don’t combine and take up one slot, making one indestructible item that can never be destroyed/targeted.