All the authors you mentioned above (not sure about Gill though) do emphesise samatha/absorption and you seem to lean towards that side as opposed to Vipassana. This is important as it shows where your faith lies. Those authors resonate well with you and I think its good to follow that faith as there is nothing worse than having doubt in the very practice we are to do every day for 45-60 minutes once or twice.

In Vipassana we take stuff appart bit by bit (dismantling a chariot) seeing the unsatisfactoriness, impermanence and non-self in all what was objectified, while in Samatha we solidify into absorptions (aka Jhanas) and follow the path of calm, joy, bliss, gladness, one pointendness and equanimity (and at some stage all these will be seen as unsatisfactory, impermanent and not self, hence let go of).

you wrote;
"In the last few weeks it's been easier to stay focused and there are probably rare moments when the thoughts don't stop exactly but just fade way back. Maybe. Kind of hard to describe. Overall my sessions seem less jangly. But never had a "wow what was that" moment. The only odd sensation is sometimes I used to get a sort of twisty feeling. Like my body was twisting or swaying. But very slight. Have not had that in a while though."

That is progress, having thoughts fall into the background is certainly a good sign. Not that thinking is bad but for samatha practice its a good thing as it means concentreation and calm is very solid and its a very powerful insight showing us that we are not that thinking mind and that thinking mind does its own thinking (somewhere in the background blabbing on its own), without me really controling it. So if Im not that thinking mind then what am I?   Am I that "knower" of this expereince? Dunno. Keep watching


Would you mind telling us more about what you mean by this "nothing happening then I stop". What do you expect should happen? What are you after? What do you crave from meditation? 
"I tend to meditate for a month or so and then get fed up with nothing happening and stop"

In my experience any practice I did so far since 2008 needed at least 5-6 months of constant daily practice to bring about some stuff, either an experience, or change in stress levels, or getting an insight, or else. One month might not be enough for the most of us (im sure there are individuals that just "get it" and get awakened instantly but those might be rare, it certainly aint me).

You do ask about noting and fire casina. Does that mean you are doubting your breath meditation and would like to try something else? Even these practices will need time (6 month or longer) and daily practice  get anything out of them. All this stuff is building a momentum, for each mind stage or mind state. 

What ever you choose its good to really put faith into that practice and give it a good try for at least 6 months before giving up on it and trying something else. 
I personally always got good results when my heart was set on the very practice I was doing, not having doubt about it but just doing the technique as designed and focusing on the mind stuff, body sensations and feeling tones arise and pass away, one by one, on and on and on.

If indeed you are experienceing "mind falling away" into the background then I think its good to keep doing what you are doing as that is a very good sign (just dont get wound up about it though and simply keep atention on the breath and calm as you did before, nothign but that breath is of any importance in such practice). It would also help if you up that sitting time to at least 45 minutes a day or at least try to gradualy get there as mind needs a bit time to really settle into concentration during each sit.

I am no expert on this (I only have my own experience) and you should hear what others here have to say also. Always get a second opinion I hope what I wrote is not confusing you.

What do you want the meditation to do for you? 

To reduce stress and help you feel more relaxed?
(Do more of what you are already doing.)

Actually, what you are already doing can cause any of the effects described below but the links indicated will help you direct your efforts in that direction.

To produce spiritual feelings of compassion and goodwill?
(Try metta or jhana meditation:
https://www.dhammatalks.org/Archive/guided_meditations/01GuidedMetta(4min).mp3
https://www.dhammatalks.org/books/BeyondAllDirections/Section0007.html
http://www.leighb.com/jhana3.htm
http://www.leighb.com/jhana2a.htm
https://sites.google.com/site/chs4o8pt/meditation-1#meditation_serenity )

To get enlightenment and end suffering?
(Read books by Thanissaro Bhikkhu: https://www.dhammatalks.org/ebook_index.html)

To get enlightenment and see the true nature of conscoiusness?
(Read MTCB: https://www.mctb.org/mctb2/table-of-contents/)

To develop psychic powers?
(Find a teacher: https://www.dharmaoverground.org/c/message_boards/find_message?p_l_id=&messageId=21664918)

Some other reason?


I also recommend doing relaxation exercises before meditating to have more consistent and productive meditation sessions.

It can also help you to get a better sense of what meditation can do, if you haven't done it before, is to try at least one time to meditate for at least one hour. You don't have to have perfect concentration, or sit on the floor, just tell yourself you will try, just once, to meditate for at least on hour. You can sit in a comfortable chair. You can peek at your timer. And you don't ever have to do it again for that long. I did this when I was a beginner and I felt so peacful and relaxed afterward that I was hooked for life. I wanted to feel like that all the time. My attitude is the meditation I do today should benefit me today. But that is compatible with any of the objectives above.

Good. If you study the sutta carefully you'll see that there is a progression that includes all the pointers you've recieved so far.  When I first saw your post I had the impression that the length of practice you have doesn't correspond to the insights you report. It seems you have stuck to what you do well, no wonder you fall out of enthusiasm for the practice.  Follow the progression, you'll probably find that you know much more than you think.