It's a very long time since I had a car with Stromberg or SU carbs, but I'll try to contribute a few ideas;
The obvious one - is the cable operating correctly or is there any slack which means you don't get full choke ?
A pure guess, but my second thoughts always go to "what's adjustable ?" (followed closely by "what have I messed with ?"
) So are the jet heights fixed on your carbs ? I know early versions you could set the height which meant a richer or leaner mixture from tick-over which may possibly affect starting ? The other thing is float height, that's critical with Webers but again I don't know how important it is with Strombergs but it's something I would check.
I've also used the aerosol sprays into the air filter to get something running but it's only been when the car has been standing for a while and the petrol has gone off. Would yours start it you pumped the accelerator while turning it over, like you can do with Webers ? I realize SU/Strombergs don't have a pumped squirt of fuel into the inlet, but maybe it would lift the needle enough to enrichen the mixture ?
Finally, as Trevor says, the fuel pump has little valves in it which might be clogged up based upon your findings with the carbs themselves. If it's an original then it is a very easy overhaul and gets rid of another potential problem.
Brian