Well I don't want your bike Kozman011, but I think you are going about the job of tapping wrong. If you already know what I am about to say then forgive me and disregard all. I think at this point you may want to remove the head to do this job more easily. I have learned there is a certain feel that must be developed when tapping or clearing out tapped holes and you must have a clear view and access to the holes. I have also learned that tapping fluid is an absolute must and not all tapping fluids are alike or work very well. Any old oil isn't good enough and is the kiss of death for taps. Some machinists make up their own tapping fluid formula, but I use a product sold by Brownells called Do-Drill. It's really meant for drilling holes in metal but also works very good for tapping. Some tapping fluids actually increase the resistance required to turn a tap and I avoid using them like the plague . When using a tap smoothness is essential, jerkiness will cause breakage. If any stickiness or binding occurs with the tap you are in trouble and increase the chances of tap or easy out breakage. Unfortunately, as you have learned there is a limit that you can push a tap or easy out and going any further WILL result in a broken tool. When using a tap in hard material not only is lubrication essential, but you must back the tap up a lot to clear out broken pieces of material. I may only turn a tap an 1/8th of a turn and back it up and go back and do it over and over. With smaller taps you can actually see the tap start to flex a bit before it breaks, but with larger taps they just break when you exceed their limit. A good solid tap handle is essential to success, not a cresent wrench or end wrench. Make certain the tap or easy out is TIGHT in the tap handle! If the tap or easy out is loose it will break. There is also a cardinal rule that is many times forgotten, or neglected, and that is to keep the tap or easy straight to the hole. Any amount of sideward force greatly increases the chances of brakeage. When ever possible I only tap holes with the work piece mounted on my milling machine so I can keep things in line by using the spindle. Lastly, easy outs sometimes expand the broken bolt as you try to get them to "bite" into a broken screw or bolt making removal more difficult. And make for darn sure your tap is in perfect condition before starting work. If teeth are broken or missing throw the tap away immediately and get a new one. Don't be penny wise and pound foolish. How much is your time and aggravation worth? For some work I do I use one tap for one hole. The material is that tough that I don't want to chance using a tap twice. I could do an entire school on broken bolt removal removal as I have learned the hard way how to do this stuff. It's not rocket science, but it isn't as easy as some would have you believe and breaking tool bits off in holes can be very frustrating. If all else fails you can have the broken piece electrically burned out as a last option. Good luck!
Rick H.