Make yourself a nice hook scraper, about 1/4 wide.
When I used to inlet my own barrels, I'd rout a rough channel, then start to fit the barrel down in. I used a #3 sweep x 16 mm wide fishtail gouge across the grain, down the sides, down the oblique flats, then across the bottom, from both sides. This entail prying against the top edges of the channel, so leave the wood 1/32" high on the sides, then rasp/plane the extra off later to restore the nice sharp top corner of the inlet. Clean it up with a scraper.
It only took me a week to inlet a barrel with this method.