I don't know how else to make it clearer that you should use ANY TYPE OF SHRINE, so you have better odds of getting the desired roll faster, but I added some caps to the bow gear paragraphs hopefully it helps.
And yes crafting a good bow takes patience. I kept some stats of my trials, but unfortunately lost the spreadsheet somehow. What I can remember though was that on average it takes ~40 shrines (aka 400 rolls) to get Tantrum + any proc. It took me ~610 shrines (aka 6100 rolls) before I got Tantrum + Knives, which is probably unlucky and then I stopped crafting.
On average you get 70 shrines total on a Fauzt clear, so for every 2 clears you have 3 shots of getting the bow basically. Hence why we use ANY SHRINE to craft.