After playing with it a bit. Picking your weapon is definitely better but it's still a slog. I have a couple of suggestions.
1. Lichs shouldn't lose rage so that they're more common. If they showed up in every/every other mission, that would significantly increase the number of murmurs you got. Also, increases number of trial and error chances.
2. Every x lichs defeated should reduce the murmur count you need permanently by 1. According to the wiki, it's 36, 60, 84 right now. It could be done in a cycling system. So first defeat = 35, 60, 84. Second defeat = 35, 59, 84. Third defeat = 35, 59, 83. That way it takes some off of both ends. Maybe to a minimum of half. That would be 90 liches killed/converted would end up with 18, 30, 42 for murmurs. It's a constant progression that way as you learn how requiem mods interact with Kuva Lich physiology through defeats.
3. Trade requiem mods/relics for lich lures. Helps in the same way as #1 does.
4. Kuva weapons shouldn't repeat on larvalings until they've cycled through or you spawned a lich.