I actually made sort of a similar part, with a 1/8" endmill cleaning up after a 1/4" endmill... with no problems or broken bits:
Attachment 364106
Attachment 364108
The chipload may be a tad high, I try to stay around .0012-.0013" nowadays, you're around .0015". I'd keep the spindle around 12krpm and 14ipm per flute. If you climb cut, it will push the chips away from the cut. I try to stay no more than .5D DoC for picketing and .25D DoC for profiling. This is because when you profile, you have full (180deg.) engagement. Also, it helps to rough the part with a 1/4" "o" flute and leave .032" skin, then come back with the 1/8" "o" flute and do the finish pass, cutting the skin off and parting the work...