I service a lot of mowers and have had to replace several cams. If it had no valve gap meaning the valves were being held open, it should have turned over easy. The less gap you have the easier it should turn over. That being said which from your description it sounds like at some point someone before you got the engine, adjusted the valves real tight to make it start easier. Because cam wear makes the gap larger the only ways they could be too tight is someone adjusted them too tight, the push rod guides are worn, or the cam bearings/bushings have caused the case to wear and, in some way, caused the cam to be positioned closer to the head which is most unlikely. One other thing to check before tearing engine down is the push rod guides, if the (plastic in some cases) guide is worn it can allow the push rod to move out of position and tighten the valves. I have seen this too but, in most cases, it will come out from in under the lifter.
These engines depend on everything being right for them to run correctly.
What I would do in this case (if the push rod guides are good) is to remove the engine and take it apart so I could inspect the cam and can bearing/bushings. Also, if the cam is shown to be worn or the relief is not working you should check the oil pump to make sure it is pumping oil good and has no wear. Because something caused that cam wear or relief problem. Another thing is to look at the cam follower which is caps that ride against the cam and make sure they are free moving.
This sounds like a worn cam that the valves have been adjusted tighter or the push rod guides have worn and allowed the push rod to come out of the indent in the lifter and not completely out from under the lifter.