I just went through the exact same thing exact same symptoms. You mentioned about spending $300 on battery, rebuids....etc I just want to clarify the starter is a recent rebuild? These were my symptoms. Would spin up ok cold and run fine. But even just warmed up it would spin like a dying battery. The starter would stall out as soon as I hit a compression stroke. With plugs pulled it spun like a champ. I went through the whole routine, new heavier cables, cleaned all connections, new higher cranking battery, checked timing a thousand times to make sure I wasn't to advanced and causing it to kick back. In the end it was my starter. the spring loaded arms that push the brushes aainst the armature were siezed so I was getting a high resisitance open across the brushes. It couldn't pull enough current to turn over a hot engine. I cleaned up the internals of the starter, freed up the arms and she spins like a champ now. I would be taking a look at the starter myself.
