Alvin is right that these engines came from 'Arrow' cars (Hunter, fastback Rapier etc). There's nothing wrong with them - the basic bits are the same as the SV Alpine. However, for the Alpine you have to find the correct front mount plate, dipstick, thermostat housing and cover, and water pump and manifolds. The Arrow engines were mounted tilted to the right rather than vertical - hence these differences. Parts from ANY Alpine series (or pre-Hunter Minx, Rapier etc) will fit.
The other pitfall is that the cheaper cars (Minx, Hunter DL) had engines with cast iron heads and the valves are in a different order so if you put an alloy head on one of these without changing the camshaft it won't run.
Some LG..... engines were iron head but as yours is running in your SV it must be OK!
One other point - I think that Arrow clutch driven plates have finer splines than earlier Alpines so check that your gearbox shaft fits your clutch.
I don't know where you can get easily drawings of the underframe, except perhaps at the Rootes Archive in Bucks. Best to find another car to look at. Do be aware that the sills and door lower edges are curved - lower halfway along than at the front and rear. Some non-Rootes sills don't have this curve. Make sure that the inner rear wheel arches are properly rebuilt and join to the sill structure or the car will sag.