You got the job done and prolly didnt hurt the motor a bit. hook the spring ,wind uop the spring umtil it is tight . Let it off until the hole in pulley lines up to the hole in the shroud. Now comes the tricky. You have to hold back the spring tension while threading the rope through. I use a couple big screw drivers jammed between the pulley and the shroud for this. Once the rope is knotted, release the stops and let the rope slowly wind up.

Well the fins on the flywheel, revolving inside the tin shroud, are what makes the cooling air to flow around the cylinder and the rest of the engine! With that part removed, the flow of air will not cool the cylinder and block, and serious damage will soon result!
Bite the bullet, and take the shroud to a mower repair place, and have it fixed. Pay the price! A tiller machine, will be expensive to replace, where as a fix will be cheap in comparison!
Maybe you didn't damage it, but i wouldn't bet on it!

Yes, running without the fan shroud in place is seriously asking for overheat damage.

If you try it yourself to hold the winder in place while threading the rope in use vise grips. I just wind them up clamp them down, thread the rope, tie the knot, and release the vise grips and it recoils back> wally wally your done. Too bad I through away about 6 housing about year ago when I dumped all my briggs stuff.

Yeah RC'S Routine is the manner in which I repair lawn unit and Chainsaw Recoils. Agree running a tiller without Fan Shroud is asking for overheating issues . Bad Practice .