1) Don't delay seeking competent medical attention regarding this. The fact that you are already experiencing numbness in addition to the pain is potentially worrisome (e.g. nerve damage/inflammation/compression). Go see your general practitioner and get a referral to a physical therapist/occupational therapist to discuss proper posture, workstation configuration, as well as exercises to do before/during/after working at your workstation. Twenty years ago when I was a medical transcriptionist typing top speed for eight hours a day with minimal breaks, I was experiencing pain/numbness/tingling in both hands. After medical consultations, reconfiguring of workstation, physical therapy-guided stretching before/during/after data entry, judicious use of ergonomic devices including wrist braces to reinforce correct wrist alignment, NSAIDs, and employer provided twice weekly chair massages, the symptoms subsided and I was able to avoid surgery. The DataHand and Mouse-Trak Evolution I still use today are constant reminders to me of that period of my life. Outside of real medical professionals with training in body mechanics or board-certified ergonomics professionals, I have personally been unimpressed by every so-called ergonomics consultant I have personally encountered in the workplace as well as almost every ergonomics consultant I have read about online. When a so-called consultant thinks a Microsoft Natural or similar is the be-all end-all in ergonomics, that should be your first clue to run in the other direction really, really fast.
2) Don't use a mouse, even a vertical variant, as you still end up using far too many muscle groups/tendons/etc. Use a good quality, well-designed trackball (Mouse-Trak Evolution by ITAC is a good example) that correctly supports the hand without pressure on the carpal area, requires very little movement/effort for cursor control and very little pressure to actuate clicks. In addition, use a forearm support mechanism (Ergo-Rest is a good example) that "follows" your arm around ensuring proper posture and to support the weight your entire arm while working. Ideally you should get a forearm support mechanism for both of your arms and have them adjusted for the ideal height for both keyboard and cursor control device while maintaining proper body posture. I looked at the CST-LTrac and suspect at least part of your problems were related to inadvertently angling your hand upwards at the wrist due to the downward slope of the case away from the trackball used in that design. The top surface of your hand should be either perfectly level in relation to your forearm or just very, very slightly angling the hand downwards at the wrist. If you are feeling any tension at all anywhere, something needs readjusting as regards to your workstation and posture. Part of the issue with using a mouse as opposed to a track ball is that at the moment of button click, your entire hand/arm/shoulder/neck is likely tensing up to keep the cursor still while actuating the buttons. With a correctly designed trackball, once the cursor is positioned where it needs to be, no contact with the ball is needed to maintain position of the cursor while actuating a button click. Click-drag is another problem area as holding down a button while manipulating either a mouse or a trackball with the same hand leads to cramping or worse. I get around that by controlling cursor with one hand and mouse clicks with the other hand on a separate device, either the built-in mouse emulation on the DataHand or the built-in mouse keys on a track-ball-equipped Maltron.
(arm position on Mouse-Track Evolution with Ergo-Rest, palm swell on Evolution helps to prevent inadvertently tilting the hand up at the wrist)
3) Assuming you don't want to build your own bespoke keyboard and the Birmingham of which you speak is in England, rent/hire a Maltron and see if that helps. If the Maltron helps, seriously consider purchasing it outright. Don't even think about a Kinesis as the position/orientation of the thumb keys when compared to the Maltron is horrible and will exacerbate any pain you are experiencing, particularly in the forearm near the elbow joint. I would recommend a DataHand but they are sadly long out of business.
(position of thumb relative to hand on Maltron)
(position of thumb relative to hand on Kinesis)
(position of thumb relative to hand on DataHand)
Ultimately you will need to determine for you what combination of medical intervention, body posture, furniture, and input device options will best serve you in terms of ergonomics.
What works for me is a DataHand Pro II mounted on the chair arms of an Aeron for high volume text/number only work. For any work requiring a lot of cursor control and the consequent shifting between keyboard and trackball this causes, I use a Maltron and Mouse-Trak Evolution with two Ergo-Rests properly calibrated for the height of the Maltron and Mouse-Trak. Additionally, I rarely use the buttons on the trackball itself for clicking other than for double-click (Mouse-Trak has one button set by default as a double-click emulator, i.e. click it once and it sends a double click signal to the computer). I control the cursor using the fingertips only of the right hand and use the left click and right click buttons built into the Maltron. When going portable (i.e. laptop away from desk), I will usually favor the Maltron as opposed to the Kinesis/Mouse-Trak combo as the Malton is conveniently lightweight, has better overall key placement, and an integrated trackball.