Drekkly, well done in performing the slump test on yourself!
It was about as I expected. A skilled therapist, familiar and comfortable with the test, would probably be able to confirm your observations as he/she could change sequence, add rotations and adequate overpressure to the right places and so on.
This suggest that you have a neurodynamic (neuro = nerve-stuff / dynamic = movement) component to the pain in between your shoulder blades. Your nervous system is in reality one continuous structure, almost like a tree (spinal cord) with bigger and smaller branches (peripheral nerves, eg. the sciatic nerve). The whole nervous system is enclosed in protective sheets, and talking specifically about the spinal cord - the outermost protective sheet is called the dura mater. When you do any movement, obviously the nerve and its protective sheets moves with you, smoothly within the spine and extremities, elegantly adapting to the surroundings. Any structure/swelling that interferes with this nerve movement, can potentially make the nerve increasingly sensitive to movement = mechanosensitive. The most classic example is a lumbar disc interfering with the sciatic nerve and that's why a straight leg test could produce shooting pain in the leg/or back, similar to the test you did on yourself.
I'm not suggesting that anything is interfering with your nervous system (ie. no neurological issues), but I am suggesting that something might be interfering with the sensitive protective sheet around your spinal cord. It does not necessarily have to be the disc, it could be any structure that lies close to this sheet, or swelling from any of these structures. I am, as Damien, quite sure that you do not have a herniated disc, but maybe a structural change to the outer parts of your disc (annulus fibrosus), or a small injury to the upper or lower endplates of the disc where it attaches to bone, or a small injury inside the disc. AMRI-scan could potentially confirm/disconfirm this, but I don't think that is indicated at this point. Personally I'd might order a MRI if you did not improve with treatment based on my hypothesis.
My hypothesis is that when you do reversed dips, you put traction through your spine due to the weight of the lower body. This traction will have a pivot point, somewhere in your upper back where the spine is supported with your upper arm muscles. I think the triggering injury is located at that pivot point. The opposing forces at the pivot point would be increased if you (most people do) have a small jerk at the point where you push yourself up from the dips. As Damian says, it could be perpetuated or in combination with a sprained/torn spinal ligament, making that pivot point more unstable and vulnerable to withstanding the opposing forces I'm talking about. Probably we'll never know.
You should have a thorough examination of your thoracic spine, not only the simple plane movements as forwards/backwards bending, rotation and side bending, but any combination of these to explore every possible movement combination of your thoracic spine. I would also recommend a thorough palpation examination where the therapist puts pressure to different parts of your thoracic spine, again in every possible direction, preferably when you lie/sit in a neutral position compared to when you sit in your most uncomfortable position. This will not tell you if its a disc or not, but should give the therapist a preference on what type of treatment to give you, and also physical reassessment markers he/she could retest directly after giving you a treatment to see if it was beneficial to your or not.
You could try to treat yourself a bit. Sit straight, chin towards chest, notice amount of discomfort between shoulder blades. Maybe even try rotation. This is your reassessment marker. Do the slump test fully, straighten both legs 10 times, retest yourself in straight sitting position. Do 10 reps about 3-4 times or until you don't get more improvement. This is to treat the sensitivity of that protective sheet I talked about.
I'm personally not too familiar with McKenzie exercises for thoracic problems, but google it. I would think the exercises done in front lying with upper body extension could potentially be of benefit to you. Try them, reassess yourself directly afterwards! Sit straight, chin towards chest and so on.
I think any therapist you see should reason along the ways you've been given here. The initial questions asked by Damien are CRUCIAL for any therapist to understand your symptoms. If you don't get this form of communication and reasoning from your therapist, ask for it, if he/she is unable to reason, move on.
Kind regards,
Sigurd Mikkelsen