Priorities...

I could respond to the last post with the following thought - we only live today, especially so after a certain age.
However, I do have an impression that the OP may not want those speakers badly enough to go into complicated and potentially costly maneuvering.
That's the point of any discussion to have different opinions that all have the right to be, not some nonsense presented as an opinion and demanding the acknowledgement as such.
Objectively, I believe there is no one 'right thing to do' here. Subjectively, that's what the OP will have to figure out for himself.

I mean these questions in a friendly way: Why ask for detailed system advice without listing a complete system?  And what are your long-term goals for the system? What kind of musical experience are you after?

I don't mean to single you out, by the way. Lots of people ask for system advice without giving full context.  Photos would help too, so as to determine whether advice is appropriate for a particular space.

Again, what are your sonic goals beyond what you have now, what are your sources and ancillaries? Without knowing what these are, as much as we'd like to, it is difficult to make educated/experienced recommendations.

As an owner of Tannoys, you do not need Gamut monoblocks to power them.  Yes, you need some clean power, but quality is the most important factor.  Decide if you want tube or ss.  As for me, I went tube pre and ss amp for my DC8s.  From my research, the 10As are perhaps the "brightest" of the upper end Tannoys. No, I've not heard them to confirm.  A nice tube amp with at least 50 wpc or a ss amp with 100 wpc will be just the ticket.  If it were me, I'd sell the Gamuts, buy a good Integrated amp and get into the Prestige line....Turnberrys i.e.  Good luck and let us know your thoughts so maybe we can be of further help.  Regards.....

Buy nothing until you know it will improve...bring delight to your music.   I would listen to your current system .....go to concerts, enjoy life.