How fast can your machine run?
That diameter in 6061 could be run at 20,000 to 30,000 rpm. Obviously your machinist's calculator told you to go too slow.
Four flute cutters are not really much good in aluminum because they do not have enough flute clearance and the chips pack up and jam the cutter breaking it; as you found.
And the feed you got from the calculator is a bit fierce for a tiny cutter. A fairly good rule of thumb is 1% of the cutter diameter per tooth, maybe less than this for cutters smaller than 1/2". This gives you about 0.002" per rev for a two flute cutter and at 6,000 rpm this would be 12 ipm.
Also coolant is more or less essential when grooving with a small cutter, lots of coolant to blast the chips out. A powerful mister with lots of air and a little bit of coolant may suffice but whatever you use you do need something to blow the chips away and give some lubrication to the cutting edge.
With coolant, running at 6000 rpm or higher, with a feed of 10 or 12 ipm you should be able to take more than .03" per pass. Taking the full .175" depth in one go may be optimistic but 0.05" should be possible and you may be able to push it to 0.0875" with the feed backed off to about 7 or 8 ipm and take a shorter time overall.
An open mind is a virtue...so long as all the common sense has not leaked out.