Can I replace a 24uF capacitor with 22uF?

Can I just replace these with one 22uF cap without hearing any significant shift in frequency balance?

Possibly not "significant" but it depends on the type of xover.
Tannoy usually voice their products very carefully and I would urge you to just replace the caps with the exact same values.

Vapor1, I am intrigued by this idea. Can the 4uF cap really have that much influence even though it is only roughly 16% of the total capacitance?

Clarity can make whatever value you need, they are very very good caps.

The Clarity MR are large caps btw.. I would be inclined to parallel 2x12uf, as the circuit was designed with that esr in mind i would have thought.

Vapor1, I am intrigued by this idea. Can the 4uF cap really have that much influence even though it is only roughly 16% of the total capacitance?

Yes, with some caveats. The Clarity ESA and MR are very similar in character, so this approach works well. If for instance you put a 4uf MR on top of a 20uf oil/paper cap, the results would be more unpredictable. I have used combination of Clarity ESA and Jensen copper foil/oil caps for the smaller value and it worked well, the Jensen character is most prevalent in that case.

For large values like this my go-to is ESA for the big part and whatever flavor on top of them. Since the ESA's are very neutral it's proven to be a solid approach.

Pretty much whatever you do though is going to be better than the Bennic electrolytics.