It is rather weak
- Dedication: it is borderline useless in a slow paced campaign, formulas are cheap, runestones are cheaper. Add an extra property rune slot to one of your items, but it only fits a rune up to half your level
- Find the Time: again, it is borderline useless in a slow paced campaign with lots of downtime
- Temporary Runes: this seems to be somewhat useful, but very weak. This has two limitations, lasts 1 minute and the rune has to be up to half your level. Champions of this level can take Radiant Blade Spirit, which gives them a 11th level rune for a full day. Increase either your time for a full day, or the level of the rune to yours. Make clear this does not count against the limitation on the number of property runes
- Rune Eater: I would not want to remove all the magic from my main item for a day for a bit1 of healing. Using a secondary item for it takes too many action (1 for retreival, 1 for Rune Eater, possibly 1 for stowing away and 1 for retreival of your usual weapon). There is probably no HP amount I would sacrifice my main weapon forfine, so just limitbut those rarely have as many runes as the usage for once per daymain items, rechargeso the runes after a round and increaseamount still might not worth the die to d12, you are paying a class feat for a 1/day/item healingaction
- Twice as Bright: probably fine. +2 (you should be able to afford two property runes by this level) status bonus to AC and saving throws is huge, but you usually do not know if you have another encounter in the next hour. If you can use this on secondary items, limit it to once per hour
I think you should just have a discussion with your DM
I do not think this archetype is useful even after making it stronger:
- If there is enough downtime, the archetype is mostly useless
- If he thinks the adventure should have such a time pressure that you do not have time to get runes in the usual way, he will not allow this archetype anyway
- If he thinks the adventure should be fast paced, but you should have a chance to get level appropriate items, he will just waive the time requirement, as mine did
- On this level you should have a +2 greater striking weapon with 2 property runes, which is 7d6 (24,5) HP. A Heal spell on this level would heal 7d8+56 (87,5) HP for 2 actions. Battle Medicine with master proficiency and Assurance would heal 2d8+30 (39)