First of all you must avoid breaking a waterpump bolt. You don't want to hassle with drilling out a bolt, so be careful not to break them. And use new bolts when fitting.
Ok, how to avoid breaking.
1992 Porsche 928 GTS Midnight Blue
There are 14 bolts total. One is hidden under the center lip of the WP and recessed. Not visible from any angle.
We managed to get it off but now have to tap and rethread that hole to get a screw back in because the one that broke off is goes all the way to the water dam on the back side. (of course that would be the one).
While drilling it out, one of the tips broke off in the hole and now is preventing further drilling. The fun continues......
Timesert preferred fix to drill and tap. (Helicoil)
This has worked for me: Get yourself a few left hand/reverse hss bits, use a
blue flame to heat and let it cool, then go slow with drill and use oil. You may
be able to spin it out early.
If you break a cobalt drill bit off inside the block, you will be close to
what I encountered in my first timing belt job when I managed to snap off a
tungsten carbide tap in one of those holes that I had drilled. Tungsten carbide
is harder than cobalt steel. What worked for me to get that tap out was diamond
tipped Dremel bits, as in Dremel 7150.
Used in short bursts (10-15 seconds of moderate pressure, then let cool for 20-30 seconds), these small bits made quick work of the tap as I cut across it in a few minutes and the pieces fell out. I only needed two of these bits - the first lost its tip from overheating. You may want to go right to that solution. It should be easy with your softer drill bit piece.
After you get the remnant out, if the original threads are destroyed, the best solution is Time-Serts. Heli-Coil, which is more readily available (sold at Autozone) would be plenty strong enough for these very low torque bolts, but may not provide the seal needed, as you said this hole penetrates the water jacket (I didn't know any of the WP bolt holes did that). The 6mm Time Sert kits are expensive.
Amazon.com: TIME-SERT M6 X 1.00 Metric Thread Repair Kit 1610: Automotive Amazon.com: TIME-SERT M6 X 1.00 Metric Thread Repair Kit 1610: Automotive
NOTE: The reason my tap broke was that I had drilled the bolt slightly off-center, leaving a small crescent of the original bolt in the hole. That steel piece caught the tap and snapped it. Be sure you are not in the same situation, as that may snap the Time-Sert or Heli-coil tap.
SECOND NOTE: I have both Heli-Coil and Time-Sert 6mm repair kits. I can Priority Mail it to you for you to borrow for postage cost (~$5) if you need either. (Actually, I need to check that later today - I may no longer have the Time-Sert kit)
As I noted above, Dremel with diamond tipped bit. Cheap and effective. And
don't think that Harbor Freight's similar looking supposed diamond-tipped bits
will do the job. They won't.
Also, how good are these "cobalt-tipped" bits? If they are Harbor Freight, then no wonder they are failing to do much.
With the Dremel idea, which worked well for me, you have to be a bit careful and develop a technique that will hole out or cut across and release the stuck fragment w/o gouging the wall too badly. If you go to Time-Sert, there is some leeway with gouges. As a final saving grace if you do botch this, Time-Sert makes the much thicker walled Big-Sert. Overkill in terms of strength but a perfect solution if you really mess up the hole in the block.
There may be other solutions that are easier, but none come to mind at the moment.
You really need a hardened steel left turning drill bit. These are specialty
items for metal workshops and costly. Remember to reverse the drill rotation as
Walton 10063 #6, 3 Flute Tap Extractor With Square Shank: Amazon.com: Industrial & Scientific Walton 10063 #6, 3 Flute Tap Extractor With Square Shank: Amazon.com: Industrial & Scientific
Did not come across such a tool when I broke a tap in my block some 10-12 years ago. After a few days of collecting suggestions here, I cut across the flutes with a Dremel bit in a few minutes.
Some tap extractors are said to work with spiral flutes, so might have some luck with drill bits as well.
If all else fails, EDM will get a broken bit or tap out quickly and easily
without touching the threads. Some machine shops have the EDM sinker system.
(EDM = Electrical Discharge Machining)