As you say , a Forstner bit is the ideal drill type to drill your angled holes - however they don't come in fractional sizes. However just as in metalwork, precise holes are reamed after drilling, so you want to open out your initial hole just a little. I would be tempted to get a cheap 30mm Blacksmiths bit that has a reduced shank so you can chuck it in a power drill. Then just use it to ream out the holes a bit by hand to get the fit you want.

You say the base is 'green' ie wet - as it dries this wood will shrink making your holes smaller. If your dowels are too snug a fit, then you might get splits, however get ot righ and you will get a tigher fit that will last better than any glue!

Hope that helps