I think the stress you are experiencing is more to do with trying to make your rewards too interactive than any other factor.
I understand managing it all makes for more work. Post more work-in-progress pictures, completed artwork - that kind of thing for lower tiers. Its less work - the art is done already - and it builds more hype for new releases. You post that directly to the patreon site and don't have to keep track of who has paid and who hasn't. Give custom things to higher tiers: its more work and they are paying for it. There are less of them though and should be easier to manage. Don't give patreons a choice in which picture or girl or whatever. Choose one and send it to everyone. Decide on your rewards in advance and package them and send them in one go.
Instead of making an API call to give out kobans post a link on patreon for patrons to follow that checks their id against a master list of patreon users on your site's api. Make it a one use link, with a unique code for each month. That way the onus of getting the kobans shifts to the user and you are dealing with the ones with problems instead of everyone. Also the patron knows immediately when their allotment comes in and there is less questions for you to field.