lots of good advice has been provided
I can add;
You need the Factory Service Manual for these cars, ( any car).
It used to be you could get a cheap CD ROM on Ebay for a few $,
but there is a used paper one on Oz Ebay atm for $60
If its a S2 with HD8, that is not original,
S1 XJ6 HD8 have diaphragms
I presume you have the cylindrical S1 ASC, not the rectangular S2 AED as a starting carb ?
Either must be fully operational or your car will be very hard to start, and run like a dog until fully warmed up (and I live north of Sydney).
If it starts easy without the ASC, its tuned way rich
I agree with other who have stated you must be systematic
(this car is new to you, and has been altered. You cannot assume some PO has not messed up)
which would involve;
triple check your plug wiring order, and that each plug is firing by pulling leads one at
a time
apply a vacuum gauge to your engine, a very good tool for poorly running engines
remove cam covers and verify timing with cam tool ($30 on Ebay)
you have already checked cam lobe clearances, so maybe you did the above as well ?
verify static timing, points gap, distributor is oriented correctly, verify engine timing at 3000RPM with timing light.
If all that checks out its time to systematically diagnose the fuel system
The HD8 is pretty simple, but needs to be taken apart, and a few things checked
do the jets move up and down when tuned ?..is fuel visible about 2mm down in each jet well, do the butterfly spindles move at all in the bush ? etc
imo, you must have an operational Starting Carb,
fix known faults first