I've no experience of the Gabapentin, but your other medication could probably do with some changes which should make a lot of difference.

The 240mg of verapamil is very much at the low end of what most people find effective, with most getting relief around 360-480mg and some needing to go as high as 1000mg. But only change this with your doctor.

Taking codeine and paracetamol for CH pain is pretty ineffective, especially the paracetamol and using codeine on a regular basis is likely to have other issues like dependency. It is pretty rare for pain killers to have much use in CH management.

Oxygen should be used as soon as a CH starts, not if pain killers don't work as you imply from your post. Using oxygen at a high flow rate via a non-rebreather mask can result in rapid aborts. I can kill mine off in about 5 minutes.

Sumatriptan 50mg sounds like you're taking the tablet form. Again this is not great for a CH as it can take about 20 minutes to become effective. It also sounds like you use this when all else has failed when triptans should be taken at the start of a CH to be most effective, with the injectable form being much quicker acting (about 6 minutes).

I'd discuss the above with your doctor to see if a few changes can make more difference.