First off, I think both Legend: Bloodline and Ravenous Hunter might both be better off in Resolve under just one single omnivamp rune, as they both aim to make the user more survivable through sustain. Similarly, Tenacity is a mechanic more fitting of fighters and tanks than marksmen, and so deserves to go on Resolve as well. Life steal as a mechanic is extremely specific and benefits only one class, as does attack speed, which is why I also think it would help to make the precision tree itself grant adaptive AD/AP, and only offer bonus attack speed via select rune options. Having takedown-based bonuses is a great idea, but might be better off with effects that benefit all damage-dealers, such as a scaling Spellblade effect as mentioned in the OP, or even some kind of Luden's/Kircheis-type bonus damage every few attacks and casts.
Additionally, in order for Precision to be worth picking on everyone, I think its keystones should stop being tuned as heavily around marksmen. Fleet Footwork does not need to synergize specially with crit, but could very well use a buff to its AP ratio to better accommodate mages looking for sustain (though this kind of sustain effect might itself be more appropriate for Resolve). Press The Attack runs on pretty much the same general rules of application as Phase Rush and Electrocute, so in this respect it might help to make it stack on abilities as well as attacks, and then perhaps put more emphasis on its damage amp, and less on its bonus damage to avoid conflict with Electrocute. Lethal Tempo is intended to synergize purely with autoattackers, and so doesn't need changes in this respect, imo.
I think one of the biggest issues with Precision is that, as a tree, it's currently designed to synergize almost exclusively with marksmen, but otherwise has no true unifying theme. There are tons of runes in the tree that, for some reason, offer sustain or durability, and would be better off in Resolve, whereas Presence of Mind would likely be better off as a competitor to Manaflow Band in Sorcery. The Combat subtree is fine as a list of situational damage bonuses, but the rest of the tree is mismatched, and makes little sense other than to offer a grab bag of stats that are especially appealing to a single class over all others. Updating the Legend row to include a more mage-friendly rune could be a good step towards opening the tree up, but I suspect a lot more would be needed to make it truly as accessible as the other trees.