I've been working as a prototype machinist for a few years so similar situation.
You just gotta try. If the tool says it can do it and the machine has enough power just work up to a good DOC. Trust the DRO and have at it. I've almost never had anything go flying out of a vise or chuck, but use good judgement.
I've made .1" doc in 17-4PH H900 and titanium on the lathe holding onto 1/4" of material. Never had a part go flying. Ive thrown parts in the mill but never caused machine damage, just broken endmills and scrapped parts.
On super expensive material or parts I'm slow but I can still hit .0001" tolerances with big roughing cuts.