Congratulations on a successful extraction.
We do tend to forget how wonderful carbide is for dealing with hard components impossible to machine by conventional methods.
Several years ago I broke some M2.5 taps. A 5 flute centre cutting carbide end mill chewed them out just fine and survived to fight another day. As usual I bought 2 following the well known workshop rule that “if you have a spare it wont break”. Unfortunately the M2.5 taps apparently hadn’t got the message. The centre cutting carbide end mills £ very reasonable from E-Bay. Darned if I can recall the breed. Nikken maybe.
A 2 mm cutter in a Bridgeport looks grossly undersize.
I think Jason is bit optimistic on how far down you can go in Phosphor Bronze before backing out and cleaning. With anything below about 1/8′, 3 mm my rule is two turns going 1/2 turn forward, 1 turn back then right out, clean get some lubrication in the hole then go a bit further. Phosphor bronze re-defines evil when it comes to tapping. I have a very nice 3/4″ rod of a darker than usual alloy that is nigh on untappable and un-reamable.
Way back I saw a lubrication tip where a guy was casting short sticks of candle wax, cutting to length and dropping them down the hole. He reckoned that besides lubricating the working parts at the sharp end of the tap the wax also pushed the chips out. I imagine that the flute base and sides would get a coat of wax helping the chips to slide. I find Trefolex is a very effective lubricant but it does tend to stick the chips to the flutes.
Clive.