I have a Stuart Taylor with a ZZR 1100 engine going into a sierra LSD
Going from neutral into first can give a clonk when hot as can changing up through the gears. I find that the quicker I change gear the quieter it is. There is some backlash at the diff but when backing off the throttle completely there is no clunk. Any ideas on smoothing it out or is this what I should expect?
Regards Jon

Pretty much what you'd expect. Its a symptom of the bike box Just listen to any bike dropping into gear. The bike cush drive mitigates it though and TRT prop helps (a bit) in a car. The 'lash in the diff exaggerates it and I don't think
the solid mounted diff helps. If you think it's bad with a Sierra diff, try a Freelander one (has loads more backlash).

I've found the same in my Grinnall Scorpion.

Being a bit higher up the revs when I change seems to make it better, as too does nudging the lever rather than pushing (does that make sense?)

It gets better I found the more I've got used to it.

1st gear clunk seems to be par for the course regardless for me

Neutral to first requires a static gear to suddenly mate up with a rotating one. It's all dog engagement on straight cut gears, a hefty clonk is what you'll get. The number of dogs may well be variable on race gear sets (to ease selection), but the clonk will always be there. The dogs will wear in time, engagement (and the security of it) may well be more difficult, some dogs are undercut (particularly on race gearboxes) which certainly do clonk as they grab.
Keeping the idle low may well help, tangential velocities much reduced.
Upshifts and downshifts require heavy throttle movements, forget the clutch, just cut on an upshift, blip on a downshift.
4-5-6 shifts will be easier than 1-2-3, just in rotation speed differences, less for the former.

Some clutches have anti-judder springs, some an anti-judder plate. Might help if you're squeamish about all the clonking. TRT tubes on the prop will help too, but (not that you'll have the issue with your unit) high power engines will destroy them. Dumping any reverse gearbox that you might have will also help with any backlash clonk. Any high power engine will have destroyed this already anyway.

Fit slicks, take the car on a track.

Typical clonk, typical clutchless upshifts and downshifts:

https://www.youtube.com/watch?v=TD-gPPnNBVM

Always get a good "thunk" as it goes into gear, the harder you push, higher up the rev range & faster shifts it's less noticeable, but it's always a bit brutal! It's one of the things I love about bike engines, it's a much more feral experience than a car engine!

One thing I did find stopped the initial clunk into 1st (which I did find slightly annoying!), was to keep the clutch down for a goodly while - this allows everything in the box to slow down & stop, you can then engage 1st without the hefty clunk usually associated with it!