Regafan:
I remember your first post from a few weeks back about your Tannoy speakers that date back to the late 80's and whether they are keepers or not.
It seems like you are looking to upgrade your system, have a very real defined budget, and are looking for suggestions as to what to do next.
The old argument about buying separates (40 years ago) was that it allowed a reasonable upgrade path and also, if one component were to break down, it was easier and usually cheaper just to fix or replace the one item. Today, audio hobbyists change out (upgrade) equipment long before a component reaches the end of its useful life.
The thing to keep in mind is that you will reach a point in audio where diminishing marginal returns set in and upgrading to a real improved level (as opposed to different) will cost a significant amount of cash ... buying new or used not withstanding.
At the $2000 level (let's assume new), an integrated is still your best bet. An integrated with main outs which allows for a preamp change would be give your more options. To your original question, my experience has led me to think that most manufacturers have a certain "house" sound, so going up a manufacturer's line gets your "more better" of that house sound. I am sure that there are exceptions.
Going back to my original answer to your post, I think the next step is to consider the "tube" option. I was a "died in the wool "solid state fan until I took a chance on the Prima Luna Prologue Two about 2 years ago. It is not that there is no going back to solid state, it's just that a good tube set-up will give you sound and satisfaction that I have not heard in many solid state amplifiers, especially in the $2000 range.
Granted my tastes may run to the contrary as I have never been thrilled by some of the speakers that are highly touted here (eardrums that have been burst several times probably helps). But I do have both tube and solid state set-ups in my house that use the same speakers, the components are all pretty good in their own right, and so, I see the the tube/solid state paths as different ways to go. It probably all converges at the $20K point or so and I have no real desire to get there.
Regards, Rich