Tom G.;
I think you would have a lot of fun and interest in a Square 4 LSR bike. In regards to the failures of connecting rods, the rods themselves were not the problem. Ariel used pressed in studs with nuts as opposed to bolts in their rods. The stud material they used would probably be considered inferior today. The real problem was, if these studs were ever over tightened once, it's not a matter of if, but rather when they will break. I've probably got every Ariel shop manual printed, even from the 30's, and not one book gives a torque spec for these studs. And because the stud material is unknown, it would be hard to even guess a torque spec.
The other problem they had was the oil passage in crank that feeds oil to rod bearings. If a Square 4 has set for awhile, the old oil solidifies and the passage plugs solid. When I restored my 1940 Square 4, I literally had to run a long drill thru this passage to clean it out. There have been more than a few old Square 4's, that after found in a shed or barn, the excited new owner would change oil, add gas, and after a few laps around the block, poke a hole in his new find.
If you find your motor and proceed with your project, I have billit H-beam rods for Sq. 4's.
Good luck and have fun,
John