Sounds like a real pain if they are corroded in place!

I looked at the parts diagram and saw where the ignitor fits in and you're right, it doesn't really show much as to how it is held in.

I'm guessing this is what you are replacing, the top burner ignitors?
Whirlpool 8053717 Top Burner Igniter - AppliancePartsPros.com

I own an older freestanding gas range that has parts that look very similar to this one and when I was having problems with it starting, mine wasn't those ceramic ignitors that actually create the spark on top of the range, it was the square ignitor control switches.
Whirlpool 3196690 Igniter Switch - AppliancePartsPros.com

In mine, they were behind what your model calls the manifold, Section 03, and I discovered 2 were cracked and due to having my elderly mom here part of the year and not wanting her to worry about it not lighting, I replaced all 4.

If those are all working, and hopefully they are because they are showing $40 for each one, without having to do any drilling of the corrosion, have you tried vinegar to remove the corrosion to get the busted ceramic tip out??

It is cheap and simple.

Remove the burner top that holds the ignitor and remove the wire.

Find something that will hold the part that is just a bit bigger around and deep enough where the stuck ignitor will be covered.

Put the burner top in and pour straight apple cider vinegar on it till it covers the corroded part.

Check it daily.

After 36-48 hours, check it and see if the part pops out. Maybe tap on it with something about the size of a punch?

I had a pair of linesmen pliers I found outside in a vacant lot, no idea how long they had been out there but they were rusted shut and solid. Nothing would penetrate to free them up. I tried putting them in a vise and driving a wedge of wood between the handles after hitting with penetrating oil a few times, nothing.

Stuck them into an old narrow Tupperware container and filled to just above the hinge point.

After 3 days they opened up and I hit them with a bit of WD-40 and they've been fine since.

Unless you are in a hurry to get them out, I'd try this trick once on one of them and see how long it takes for the vinegar to cut into the corrosion. It did not hurt any of the other metal, just cut into the rust.

Hope this helps and good luck.

FYI, I ended up using a Dremel tool to grind off the tops of the burner screws so I could get it all apart. The square recess on 6 of the eight screws was rusted to uselessness. Grinding took a long time - later I discovered that it was possible to grab the the other end of the screws with vice grips and turn them enough to break them loose from the rust. I replaced them all with 8-32 x 1/2 stainless steel button head hex recess screws.

PB Blaster corrosion dissolver and vinegar had no effect on breaking the screws loose.