Go Active Crossover or Upgrade existing XOs?

George's work was for naught.

Only to those with no ears.

@pizzano may I ask which technology you used for about $300?

IMO there are many speakers with passive crossovers indeed but just a small amount of these are implemented right, that's why there is an aftermarket modding it. There are many challenges with passive (impedance changes, phase etc) that only experienced designers are able to make it work and this represents adding more elements in the signal path and with digital dsp advances, passives will fade eventually.

Answering directly to the OP @gadios, I will definitely experiment with active or active digital if budget allows it (and time too). In my specific case my speakers have passive crossovers but to my ears I like to think are well designed.

I am not an EE, or audio speaker or amplifier designer, just another guy who likes music reproduced in the best way possible.

Depending on the number of drivers you have (remember you'll need an amplifier channel for each one) you could look at one of the MiniDSP solutions. If you have three way speakers and are on a budget you could start by replacing the Mid / Bass crossover and leaving the Mid / High intact which would require a DSP with four outputs and four channels of amplification.

Please remember 85% of Xovers in speakers unless very $$
are substandard.i have been modding Xovers and internal electronics for over 25 years. The Xover parts usually at best have solen capacitors or the China specials Keven speakers at $10 k +
shocking but true I had a 15k Martin logan ,and Sonus Faber 
both had the lower quality white mundorf evo caps.
in your Tannoy he Jupiter copper foil would be excellent 
and use the worlds best resistors from path audio.for my audio get together I demonstrated a experiment a stock monitor audio studio speaker, and one I added $1000 in Xover parts upgrade
it went from a $1500 to a $5k speaker in sound quality vs several 
well known speakers . The Xover is the brain,or heart of all speakers, also buy good WBT Copper connectors not the junk 
gold over brass which comes with most speakers .brass is horrible in natural fidelity vs Copper and has 4 x the resistance = distortion 
i spent literally 1,000s of hours listening and comparing .i usually also replace the cheap internal wire as well as jantzen a Copper inductors . When using a electronics active Xover you can tune it but it looses the flavor of the great capacitors which adds that depth and live presence Lon paper a active is more ruler accurate 
thst applies to solid state vs vacuum tubes in accuracy but 
having a vacuum tube in the circuit adds another dimension in realism. Your ear is the final word in tonal accuracy thst is whst I rely on more then just measuring equipment ,which is just a guide or starting point. After 40 years in Audio and having owned a Audio store .i have had pretty much most things out there learned from many excellent techs on modding .that is why modding 
gives back so much more per $$ dollar spent in fidelity vs just buying new ,for rule of thumb  25% or less  of the product cost actually goes into the parts ,the rest overhead,R&D,and overhead!!

I've been running an active crossover system for nearly thirty years using four ARC amps. Two mono blocks for woofers and then two stereo amps for the mids and highs.  Probably the greatest advantage IMHO is that none of the amps "know" or could care what any other amp is doing. Tons of headroom. If you like to twiddle the knobs its Christmas everyday!  Plus really fun to only run the bass amps to tune the room etc etc. 
The new PS Audio AN3 is a bi-amped system and sounds amazing to me. Arnie Nudell's large systems were bi-amped as well.  Does anyone remember the M&K sub-woofer satellite system way back in the day? BTW, the ARC room at RMAF was a true bi-amped system using three
ARC amps, two mono blocks and a stereo amp powering Sonus Fabers.
All analog system, no digital in the room.  To the OP I say "jump in the water is fine".