Your timing can't be too far out, or you'd have trouble starting and/or running. Let it warm up, then advance the timing a bit to see how it idles, then retard it to see how it idles. Find the best spot you can, then see if you can lower the idle speed a bit. Keep fiddling until you find the lowest smooth idle you can achieve. Turn it off and restart - easier or harder restart? Adjust as necessary. Advance enough to get some plinking, then back down. Obviously not as good as actually seeing the timing, but should be in a safe range and good enough for the first round of adjusting the carbs.
Double-check the diaphragms for holes and the pistons for easy movement, and make sure they fall freely and close fully with a click. Check the butterflies, are they all fully shut with no throttle? Fully open and parallel with full throttle? Do they close with a click when the throttle is dropped suddenly? Any obvious differences from one to the next?
How are your carburetors attached to the engine, what type of manifold? The Elan has a Federal version with emissions equipment or Euro version with balance bar - not sure whether the Europa is the same.? Soft mounted with thackeries/grommets, or hard-mounted? Appropriate gap between carb and manifold?
Check for vacuum leaks at the manifold and adaptor plates or any take-offs, as well as where the throttle spindles come through the carb body.
Keep going back to timing and throttle screws, looking for a decent idle at 800-1000 rpm. It will be a bit lumpy with Strombergs, but should hold steady without needing to blip the throttle. If you can't get there, its time to go further inside the carbs. If you can, then start checking out where things stand under load and with partial and full throttle.
What needles and pistons are in the carbs? Are the needles adjustable? Do the needles show wear? How about the jets they slip into? Wear on either/both parts will contribute to richer conditions. Perhaps the idle mix screws you found open were opened in an attempt to lean things out? Are the floats correctly set for the right fuel level? Is the fuel valve working correctly?