I'm certainly tempted as it looks like Royd sourced their components from Tandy and the cross-overs are in an external box.

I upgraded the crossover on the Hawthrones but this was a DIY based open baffle and read good reports on the forum.
Later I changed the tweeter and had to make slight adjustments

Very nice Chris, what an excellent job you did with those Genexxas.

I'm thinking along those lines - better quality crossover components and some work to improve rigidity of cabs.

Of course my ailing power amp will have to come first! 

I was, but both companies who were offering component kits have gone silent.

It'll remain a rainy day (after I retire) project.

I think this really depends upon the sound quality of the speakers and how good the overall design including the crossovers was in the first place. Another aspect is if the crossover components are getting a bit old in the tooth, 15-20 years maybe, then it may be best to either replace with equivalent spec crossover components or if known improvements can be had to improve the crossover, but as I have been told by a couple of speaker designers and repairers it is often not straight forward. 

I used to have a pair of Impulse H2's and these have a known crossover issue at around 550hz, if I recall correctly, that causes a drop out, A repairer who was very familiar with them over many years advised this was very simply rectified with a £1 resistor in each crossover but to do it right needed accurate measurements to be taken of each speaker and then ensuring the result was a matched pair. However others would advise on replacing the crossovers and upgrading the tweeter, much more costly. I also found out that there were variations in the crossover design and placement of them over their build life, so it was clear that it was not that clear cut. I talked with a few owners that had taken both routes mentioned, interestingly the first route seemed to be liked more, the second route had moved the voicing of the speakers away from their original sound and some had then sold them and gone to another speaker design. I leave you to make your conclusions on this. 

I also had an original pair of JLB L100s from the mid 70's, they actually sounded rather good with the original crossovers and variable pots which still worked fine. I investigated upgrading or changing the crossovers, and once again came across various views, from leave them as they are to just remove the pots and to throw away the crossovers and replace. Once again reviews of all approaches seemed to fall into two camps, minimal changes to the original spec was best, just replacing/upgrading components with removing the variable pots and setting the crossovers to the original neutral set up, the other camp being throw the original crossovers away and install a different specification. It seemed the overall outcome/consensus was similar to the above. 

Personally I think if the speakers work well with your amp and you enjoy the overall sound then leave alone. If they are a bit old in the tooth then I would replace resistors and capacitors to the original spec but possibly of a higher quality, doing much more is likely to change how the voicing and you may not like that, I suppose you could always revert it. 

Clarity caps and Millers resistors are safe bets. Leave inductors alone.

I was planning on matching the design and specification, but using good quality components. I will leave the originals untouched as the housing can just be unbolted from the bottom of the speakers and they are connected to the speaker drivers by fly-leads to sockets in the back of the cabinets. I will change the connectors though as they are pretty crap and one is broken (and a pain to fit the speaker leads into).

That means I will change the inductors as well and I can try a few variants with regards suppliers. I have already bought decent fly-leads to use.

The speakers are working fine and sound good despite their age and so there is no urgency: it would just be an interesting, and relatively simple, project.

Room correction on deep bass is good.
Bad on everything else in my experience.
Hopefully they are evolving and getting better.