Buying tubes doesn’t guarantee anything. You can still have the same exact problem with tubes in the chain. If you're looking for a "warm and smooth" sound, you can just as easily get it with solid state.
Looking at the Jade 3 bright/harsh issue, most of the suggested fixes, are in some way looking to cover the problem up, not fix it. Rolling off a speaker with other components does nothing to resolve the underlying issue. Most of the time, problems with high frequencies, comes down to a matter of timber. For example, cymbals don't sound like cymbals, they sound like someone dropped a piece of metal on a concrete floor. The proper fix would be to make the cymbal sound like what its supposed to. Do that, and you'll have a system that plays fully extended highs, without sounding bright/harsh.
Yes, I agree that getting tube amplification does not guarantee anything, and I am fully aware of that. As a matter of fact, ANY ACTION does not guarantee anything, not even getting new speakers. In the end, it will depend on the listener's expectations in getting the sound that he wants from his system.
For wim1983's case, he can choose to fix the issues of his system in many ways. For me, it would be in the order of the room/speaker placement > speakers > amplification/source > accessories (cables and stuff). Usually there is not much that can be done to the room as most room acoustic products have low WAF which will look out of place in most domestic listening environment. So it's usually down to speaker placement, loudspeakers and then the electronics.
Let's assume wim1983 chooses not to go with tube amps and opts for a new speaker to replace his Jade 3. There is no guarantee that the speakers will work in his room, even if he has listened to them in-store. Having said that, I agree that getting the electronics to "cover up" the problem may not be a permanent fix, but sometimes that can actually be a fix to compensate for the imperfect listening environment/room acoustics. The room itself is the biggest factor that gives coloration to the sound or the system.
In summary, for wim1983's case, if he feels that the sound of the speakers (although bright) is still within the 90% of his ideals, he can still consider to tweak the system to make it work. The caveat is the experiment can turn out to be a costly affair. Otherwise, get a new pair of speakers and start all over - which in turn may not necessarily guarantee 100% satisfaction. In the end, it's all about managing expectations.