Geometric cutout, need help w/ tight corners

I’ve got this project in Easel with lots of angles that have tight corners.

Wood thickness is around 17mm.

I’m doing a rough pass w/ an 1/8" bit, but I need a 1/16" bit to get tighter corners. Unfortunately the depth of the wood is greater than the depth of the 1/16" bit. As the bit plunges further, it eventually hits the collar on the bit and everything freaks out/locks up/ends in misery.

How can I get those tight corners on wood that’s deeper than the depth of the bit itself?

(For reference, it’s this 1/16" bit from Inventables)

The problem with longer bits that are that small is bit flex. You can buy longer bits, (check Amazon), but you have to be careful with your feeds and speeds; you’ll need to slow it down. Longer bits break easier under stress.

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Look up Drillman1 on eBay. He has some 1/16" bits that are a little longer, but like already said they can flex more.