Burzeen, the Octavia Mk2 can hardly be considered inherently 'bouncy'. They feel well planted. Whilst not a racing car, they are a performance car and of course the VRS features in the range too, which is rather like SKODA equivalent to a Beemer M series. The engines behind them are essentially the same except how they are tuned. But even the least tuned model should not feel bouncy,, at all. The purpose of the shocks is to control the reaction of the springs when going over bumps, otherwise you will have an unpleasant ride. It might be that you are simply seeking or now favouring more the kind of drive you are getting from your Hyundai i20. Its hard to tell with a limited history about how you experienced developed over "quite some time". Clearly something has happened that was not always the case or you wouldn't have noticed it.
My experience, with the VRS at least, is it's significantly harder than the standard 2.0 TDI 16-Valve. It's very hard to understand how, upon swapping out all the parts you indicated, that you could end up with a situation that has not markedly improved. Perhaps your suspension was not worn out at all. If the new suspension is so much the same, its hard to arrive at a different conclusion. Thinking about it a little, I wonder if your experience might benefit from a modest lowering kit. You speak of 'bounciness' but to me that's something subjective. I tend to speak of hard medium or soft ride. It would be a soft ride that would most give rise to perhaps the condition you are referring to. Some people would refer to wallowing, or feeling imprecise as being soft. The VRS feels much harder than the standard Octavia. By replacing everything like for like with OEM or OEM manufacture, one would expect characteristics to be the same, as you have found. If you had perhaps changed the suspension after describing your requirements, in a way that any number of knowledgable people here may have suggested but didn't (Why weren't they excited by the challenge of the case?).
Changing suspension is a question I myself am researching. I'm trying to acquire the knowledge, so I may better understand the options and read the experience of other users. I'm hoping to discover the best value suspension upgrades to improve stability. So, yes, I'm looking for firmer still and perhaps, but hardly slightly lower. But I'm not looking for much lower. In fact I'm looking for the best value lowering. In other words I'm not looking on price. I'm looking at value for who is offering what kit. And of course 'value' is another subjective word. As to the performance of your Octavia it is mysterious. Its almost like what one would say they would expect the car to feel like. if its shocks were shot. If your shocks were shot and they were not really replaced, then your car would of course emerge from the shop performing the same way, except perhaps the new springs might feel marginally better. Once again, not much happens with springs that should be of any concern unless you break one over a bad bump or pothole. You will usually know about it. Springs are incredibly robust. Over last twenty years the technology that has gone into spring making has improved the durability of springs immensely. But a spring does not offer any sort of performance benefit per se other than smoothing out the harshness in the road and suspending the car on its wheels and by a product of the length of the spring. What you get from a spring is just spring. It might be clever spring or progressive spring but its just spring. Your car's manufacturer thought a lot about springs because it has to make sure the car could work anywhere and return great performance. It may be that you became tired with the performance of your shocks over time. Its a little difficult to determine the exact circumstances that lead to you owning a car with the difficulty you described. How much harder was it it when you bought it? Have you used your car for towing?
Getting away from the subjectivity is difficult because its most of what we perceive as a result of using our cars. Our engagement is very much a subjective one initially at least. One needs to rationalise the key concepts, such as hardness or softness of suspension. One might refer to responsive shocks which I suspect is a shock that operates differently at different parts of its stroke. Members may correct me precisely what the shocks are going apart from damping the push pull effect the springs are exerting on the strut. The idea being that if one has pulled all these parameters together such that the operation of the suspension is tight, then you are no doubt approaching the ideal. It can be tight and hard or tight and medium, but one is unlikely to run a tight strut in a soft spring. That would seem bizarre but I suppose there are some people who might want to do that in say America or Canada or perhaps Australia. Most people who want performance will no doubt be best advised to seek out a coil-strut combo if you have that kind of strut. Using a kit which means the components have been judged by the manufacturer to provide a good value benefit would be your starting point. After that you may decide, upon reading further, that you want a slightly different strut or spring as to what is in a particular kit.
What did happen over your case in the end? Did you ever consult a dealer or an indie workshop? It would be fascinating to know the answers to some of my questions if you ever get back to this! I included a picture of my work car and you will see it is sitting quite low but not so much you would notice it and feel it was too much.