what if.... you make it a 3 tier money structure? i mean.. you want money to go into religion and not as bank.
global treasury <--- as old
local treasury <--- only priests (elders too?) can take money out from that, income from peasants go there directly. anyone can put in there.
strongbox <--- where nobles get to use it as their mobile bank.. but with a fee and subject to the usual thefts (by priests, who dump it in the local treasury no less)?