I feel the Materia system can offer an ideal solution to that. All they need to do is give it a 100% chance to meld and a 100% chance to be retrieved (actually, on the subject of melding... "Increased Meld success rate" would be one hell of a stat, we actually have something similar for Desynthesis already...), then it's a trade off of what? Some minimal Direct Hit loss? Makes melding a bit more of an active process, rather than the meld and forget process we currently have. Slap on a Treasure Hunter stat before doing some more casual content (where, lets be honest, the additional combat stats don't matter in the slightest), take it off and put back Crit or whatever before raiding where Treasure Hunter has no real purpose. Arguably that's a negative, since you'd be using up more combat materia re-melding, but from a market perspective I'd say that's actually a positive?
For a Relic though, I'd say just make it the ultimate weapon for that expansion, with all the special stats... A branching upgrade process where you pick what content branches you want to complete. Don't Raid? Well your Relic never reaches the highest item level. You do Trials? You upgrade the Relic with Trial specific stats, also do Treasure Maps? You upgrade it with Treasure Hunter or something. You get out exactly what you put in, and you can end up with a weapon that's truly deserving of all the fanfare a Relic weapon should have.
Simple, all SE needs to do is revive Combat Levequests. Honestly Hunts should be special "endgame" Levequests to begin with... Done. Now the Hunt spawns because you did the Levequest for it, and the Hunt that spawns is claimed by your party and your party alone. The entire server (or datacenter now, I guess) does not, and cannot, swoop in to help you kill it. Slap in a progression system; Do the B Rank Levequest, get item for the A Rank, and so on. Make it so you can't just spam them. Now its a system you can log in and do with your friends, rather than having a schedule dictated to you by Hunt LSs.
Honestly, if I could make one change to fix Eureka, it would have been just that. Change the FATEs to Levequests. Same deal with Hunts, same deal with almost any open world content... World bosses should be a rare exception, not the bleedin norm...
This is why I like the idea of a branching Relic quest, one where you fill out the branches you're interested in. It would have branches for almost every piece of content in the game, but none of them would be a requirement, just a case of "You obtained the Trial weapons, so you can boost your Relic with them", with that particular boost being specific to Trials (maybe it has an extra Totem drop for you, helping you grind additional Trial weapons and/or the Mounts, for example). If you do everything though, then it truly is the ultimate weapon. It would have stats for every piece of content in that expansion, be a relevant weapon for all of them. If you don't like Deep Dungeons though? Well you'd have no need for the effect adding a Deep Dungeon weapon to the Relic would provide, so there's no problem, right? All those content relevant stats could be on their respective weapons, for example. Someone who only Raids gets the Raid weapon, they don't need to merge it with other weapons via the Relic because they don't care about that other content.
Arguably the existing Relics did already achieve "best weapon" status. They eventually reach bootleg Raid weapon item level, and have additional substats to boot, making them by far the best weapons. It's just... That's so boring... There is nothing exciting about seeing high levels of Crit on a Relic weapon for me... I'd be much more excited by stats like "Treasure Hunter" that do something different. If it elicited any response from me, it's the same response as upgrading any piece of equipment, upgrading a weapon from i440 to i450 is the same as upgrading from i450 to i460 in my mind, and Relics have always done the exact same thing... There's nothing different or exciting about them, which I think a Relic type weapon should have... They should be special for more than just their glamour glow.