Seized & snapped bottle cage bolt – options?

I tried to remove a bottle cage from my titanium Tripster ATR frame the other day… and the bolt snapped at the head.
So I drilled a hole into the bolt remains and then used a reverse-threaded screw extractor to try and back it out. This is the result:

What are my options now? I have a chunk of steel in an aluminium bolt in a titanium frame.
I've tried using a punch to rotate the remains of the screw extractor so that I can back it out, but have had no success so far – it seems to be jammed.
So I drilled a hole into the bolt remains and then used a reverse-threaded screw extractor to try and back it out. This is the result:

What are my options now? I have a chunk of steel in an aluminium bolt in a titanium frame.
I've tried using a punch to rotate the remains of the screw extractor so that I can back it out, but have had no success so far – it seems to be jammed.
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The broken surface of the extractor is very angled, so I think the drill bit will just wonder off to the side if I try to drill into it. Normally I'd use a centre punch to start the hole, but even the punch just slides over the surface 😕
You can get multimedia drill bits such as the Bosch Blue Granite which are carbide tipped. These should do the job
https://www.amazon.co.uk/Bosch-HCBG600T-6-Piece-BlueGranite-Carbide/dp/B0000TZYZ2
Not cheap as you may have to buy a set to get the size you need.
One final option is to just try a basic masonry bit of the required size. They won't last long but they're cheap enough that you can buy several if you need them.
Just be aware that the broken screw extractor will be brittle and could send shards flying as you drill so wear gloves and face/eye protection.
Once you've managed to drill out the extractor/screw you need to remove the damaged rivnut and replace it. This video shows one approach to removing the damaged rivnut using a Dremel, that seems pretty neat. In the video he's demonstrating on a carbon frame. With your titanium frame you have lots of leeway
https://www.amazon.co.uk/Big-Gator-Tools-MDG1000NP-V-Drill/dp/B00CYNOFM0/ref=asc_df_B00CYNOFM0/?tag=googshopuk-21&linkCode=df0&hvadid=309954591991&hvpos=&hvnetw=g&hvrand=18219700974001306192&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9045921&hvtargid=pla-490923365668&psc=1
That almost always works with a tap but theyre slightly weaker.
N
al has the highest coefficient, i.e. compared to steel and ti it'll expand more as heated and shrink more as cooled
heating the exposed end of the bolt/broken extractor will tend to loosen the extractor, the tip of a soldering iron or a fine gas torch might do it, then try to back out the extractor (i'm assuming the frame is bare metal, don't try this if it's clear-coated!)
freezer spray on the bolt might help loosen it in the mounting, but the chances are it jammed due to galvanic corrosion (the al corrosion product takes up higher volume, in a confined space this jams things tight)
you can use chemicals to attack the aluminium, but if you can get the extractor tip out, easier drill/grind/file it out until it's weak enough to break up and remove
with al fixings in steel/ti it's advisable to use an anti-seize paste (which should be a zinc-loaded one for al) to protect it