Hi sklpns,
 

> Would it be remotely possible, using FET or, maybe, inline javascript 
> plugin, to somehow automate the process?
>

Sure, but at that point I would stop trying to stuff it into FET,
as it's far too inflexible and cumbersome.

gather the monthly data with fet
>

The first problem I notice is that you never even talk about years.
At what point do you need to take that into consideration?
Anyhow, I would calculate that with an inline script.
Much simpler, and easier to read.

Also, do you really need (hidden) data?
Why not use generic slices or even fields?
Wouldn't that be cleaner?

click a button to update the content of the tiddler which holds the graph 
> data
>

That should automatically update when you open it,
unless you want it to only render at the click of a button.
 

> http://charts.tiddlyspace.com 
> <http://www.google.com/url?q=http%3A%2F%2Fcharts.tiddlyspace.com&sa=D&sntz=1&usg=AFQjCNHtHsjh2UW2pd18NGaWCwfrgomYnw>
> automatically update the tiddler that holds the graph and view it?
>

Same as above.
I never worked with those charts, though,
so I'm not sure what format they expect precisely,
as you seem to want multiple bars per month, i.e. table rows.

Perhaps you try to figure that part out yourself, first,
e.g. construct a demo table and see if you can
get that plugin to show you a meaningful graph?

Best wishes, Tobias.

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