Good question - you described me and the other two finger warriors very well!

Can't offer much in the way of suggestion except to say I've found it beneficial to use an adjustable sit/stand desk and change position regularly.

I've also trained the 'other' hand to use a mouse as well. I changed to a new ergo mouse when I had a broken thumb, and as a random finding I now use two - one mouse permanently on each side of the keyboard - they work independently and there's only one pointer/cursor so I change hands frequently.
I also mouse click more on say Word or Excel now - I'd previously been pretty good at using the MS shortcuts - but I found they mostly required two fingers anyway...

What about trying voice recognition software to reduce the need to type?

I find a wine or two at the end of the week an excellent remedy. So far so good - no OOS claims from me yet.

The problem with two finger typing is that only one of them spells...

I recommend googling mechanical keyboards. You can set them up with more or less range of motion and pick to have a satisfying click or not.

You can get rid on your number pad to bring your mouse in closer and prevent wrist rotation.

Be careful however as you can very quickly be spending hundreds of dollars.

Lots of good suggestions but how about learning to type! There are lots of free online programs, I did this years ago and have been benefiting ever since. Yes its a time commitment but think how much time you will save in the long run :)
Training your non-dominant hand to use the mouse decreases the stress on the dominant hand. I would recommend having a mouse each side to start with and do a little each day.

It's not about me. There are thousands of people who cannot touch type who sit hunched over their keyboards yet all advice one reads on keyboard ergonomics is aimed at those who can touch type. My point is what advice is there specifically for those who cannot touch type, other than telling them to learn? Voice activated software is probably the best option but if you cannot access that how does someone using two or three fingers, watching the keyboard, looking up and down at a monitor, work in a manner that does not expose them to long term discomfort or injury?

↪Ben Thomas
I know I see the two finger typists everyday and can see their frustration, and I feel frustrated watching them! I agree ergonomics does favour those who can type - a gap in the market for some to exploit maybe :). But a computer is tool and needs to be used effectively - you wouldn't try and use a chainsaw with one hand so why do people struggle for years typing with 2 fingers....?

Loving all the feedback you have already received Ben, most of it is pretty good (including the wine at the end of the week!) I am an ergonomist, and I agree, the 2-4 finger typist brigade do struggle a good deal with positioning and comfort. I could of course offer you a full workstation assessment to go over all the tips and adjustment options... But here's some for free :) (you're welcome).

1 - Learning to touch-type is a darned good idea. Try Mavis Beacon's online material. If my cack-handed hubby can get learn to do it, there's hope for everyone. And the various voice recognition options could be sensible for you as well (or a good, old fashioned secretary!) I continue to sigh and mutter because keyboard skills no longer appear to be taught at school - a sad loss, though input options are now many and various.

2 - There is a keyboard layout called Dvorak - that is different to the standard (ubiquitous but very un-ergonomic) QWERTY option. This is the one that spells 'qwerty' along the top left row. It was designed like this as on good ole typewriters this order of the keys meant the mechanical bits were less frequently 'tangled up' when in use. (But perhaps only us old girls that actually learned to type on typewriters will remember this...) Qwerty layout is demanding biomechanically for users. You have to have quite a coordinated pinky finger to hit the 'a' for instance... and that is the key on my keyboard that I have used so much that the letter has actually worn completely away. Dvorak has laid the keys out so that it is much easier to use the most frequently used keys, and also much faster - you tend to alternate left and right hands for instance when going vowel/consonant/vowel/consonant. You can often alter the keyboard layout through the setup options on your computer - my son did this on his laptop really easily. Bonus is that most people will be put off nicking your gear.

3 - Left/right swapping for the mouse... great idea. Make sure you change the click buttons on the left one so that the 'main clicky button' is used with your index finger - most brains find that the fastest change to adapt too.

4 - For the 'hunt and peck' two finger typists, make sure the screen isn't too high, as it makes the up and down with the head/eyes task really hard work. If it isn't too high you can do more of the work with your eyes. Depending on your glasses... Which can become even more problematic once you get to reading glasses stage...

5 - Sit and stand options also great. Make sure you get lots of cardio and stretching in too. We weren't designed to be 'desk statues' so keep moving. This will help to mitigate the effects of awkward postures.

6 - Use a wrist-rest and definitely ditch the numeric keypad if you don't use this heaps. A narrower keyboard without the numeric bit saves space on the desk so you have more room for your two mice.

7 - Pay really good attention to your chair setup and desk height. If you are feeling really scrunched up and sore you probably haven't got this right, and your shoulders (and probably wrists) are doing much more work than they need too. On my website (Optimise Limited) I have a cheat sheet freeby download for how to set yourself up. The correct position might be many miles away from what you think is right.

8 - There are a number of professionals working in the health and safety sector that will have specific skills in assisting people (including you) to work comfortably at your desk - occupational health nurses, occupational therapists and occupational health physiotherapists with specific skills in this field can be contacted (and ergonomists). You can find them on the HASANZ Register.

9 - And check what your risk register identifies... often this stuff is overlooked - sure it doesn't kill you - but it can make you darned sore and will impact on your productivity and overall well-being. How are you managing it?

One of the problems with the "how about learning to type..." answers is that they don't work for everyone. I've never learnt to touch type because I have a congenital defect in both my hands - so I'm a two-fingered typer by simple necessity. My typing speed roughly matches my composition speed, so it works.
I don't hunch over my keyboard to type, and I am aware that even touch typers can develop aching across their backs from poor posture.