Depending on a few things, the battle your fighting is due to you need a 168 tooth flexplate. the smaller 153 is used on dirt low compression, small cubic inch engines. you have to remember, the starter and flexplate combo is gear reduction, since the flexplate is large and the start gear is small, the more teeth on the flexplate the more reduction and the more reduction the easier it is on the starter to turn the engine over. I had to deal with a instance like this long ago, a 153 tooth flexplate and starter were installed on a high compression 350 engine, after it got to temp, the starter would drag trying to start it, didn`t matter what you did either. Monster battery, excellant cables, tried it all to no avail. That`s why I say it depends on a few things, if your 350 has a decent compression ratio the starter is straining it`s guts out trying to turn over that much mass due to the small flexplate. One last thing I can recommend to do and check over and if the problem isn`t solved I would move up to a 168 tooth flexplate and a staggard mount starter.
Check the distributor mechanical advance, make sure it`s not sticking open, make sure it don`t stick period, as I`ve seen some have 1 hard spot.
Improve the grounds. Grounds are often overlooked but are very important. A ground to the alternator bracket don`t cut it. I run a ground directly to the block and clean the grounding points. I run another ground from block to frame. I make sure all the factory grounds are present and connected. Make sure there`s a ground running from the firewall to the engine also. Sometimes the main starter wires that have a fusible link become corroded internally and this lowers the voltage going to the starter, replacing them corrects the problem.