These days old carburettors are often built from slightly mixed collections of parts, so we have to do the best with what we have!
My AMAC book gives model T. 15MDY and T. 15MDX as 1928 touring models with bottom and top feed float bowls, respectively, so maybe the "4" you quote is a mis-read of X or Y? Equivalent 1926 and 1927 models are PJY and PJX. "15" refers to 1 1/8" throttle valve - sounds about right for a sv 500.
Anyway, the plan should be to get the fuel level just below the top of the jet. From your description it sounds like this can be done - even if you need to modify the notch on the float needle or the clip on the float. An easy check for about the right fuel level is that the carb shouldn't drip if the bike is upright, but begins to drip if the bike is leaned over away from the fuel bowl. Test this with the throttle open (no needle bocking the main jet) but the engine not running!!!
Hope this helps. I can copy the parts list, but I doubt it would be of much use.