Current flow doesn't like heat. The hotter wires get the more resistance to current flow, higher ohms. I put three stock new starters in my 69 GTO and each of them dragged when hot. The gear would engage the flywheel but it wouldn't turn the crank fast enough to start. Too much resistance when hot.
Not only a hot starter but the wires going to the starter as well. A stock 68 has the cable from the battery, the purple wire from the start switch and the yellow wire from the starter to the distributor. The purple and yellow wires go down the tube bolted to the back of the block to protect them from heat. If your goal is to keep the car stock looking you could try changing the wires to heavier gauge wire, may help.
I put a high torque mini starter on my 68 Firebird and it works flawlessly cranking my 10.5:1 464 cubic inch engine. I also eliminated the purple and yellow wires and remove the steel tube they ran through. I have an HEI so I don't need the yellow. I installed a ford style starter relay on the right hand inner fender close to the battery and ran the starter cable from that, then put a jumper between the starter's solenoid and the starter's cable terminal. The only time the starter cable is live is when the switch is in the start position and the jumper automatically engages the solenoid. I just did a 1777 mile trip to central Alberta from the west coast, it was 105 degrees in the badlands and dinosaur valley, The starter worked as it should every time I hit the switch.
The nose of the mini starters is smaller than the stock, it will not fill the hole in the bellhousing cover. I cut and shaped a piece of aluminium to cover the hole. Obviously I'm not concerned about originality under the hood. Looks pretty stock with the hood closed though.