I got snapped off bolts/studs out twice before without removing the manifold. I made up a bushing that had the same OD of the bolt (or ID of the manifold hole). In the center of the bushing i drilled out the ID of the bushing with a 1/8" drill. The bushing was my drill pilot for center drilling. I drilled the broken bolt with the 1/8" drill about 3/8" deep.
Then i drilled the ID of the bushing for 1/4" dia. And drilled again the broken bolt using a LEFT handed drill bit 1/4"dia. While drilling it, in reverse, The drill grabbed the broken stud and backed it out for me. The second stud i wasn't so lucky and continued to drill to 3/8" deep using the 1/4" lefty drill. I then made a new bushing with an ID of the "easy out" OD diameter. The new bushing was to ensure i was straight with the "easy out" and to help against side loading. I got that bolt out as well.. Lots PB on both.

Be careful not to snap off a "easy out" If you snap it off you will have a bad rest of the day.. They are so hard that you can't drill out and you are done

I did this on a old f150 gasser 302ci. 4x4 mudder. Not sure if our trucks have room for a drill through the wheel well.

Just tossing out the bushing idea. I am always making bushings to aid in such things.. 10 minutes on a bridgeport or a lathe making such helping tools can save hours.