You are correct that the starter solenoid sticking is the likely issue but if you replaced this and it is still doing it then we need to take a step back and start checking voltage to find out if this is being commanded on by a sticking relay.
https://www.2carpros.com/articles/how-to-check-wiring
https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit
If you look at the wiring diagram below you will see the wire coming from the battery. This should have 12 volts all the time.
The other wire coming from the relay, should only have 12 volts when the key is in the start position.
I would put my meter on this wire and ground and start the engine. If the 12 volts stays there when you let the key go then you have an issue with the relay most likely.
Please run through this and let us know what you find. Thanks
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Sunday, September 26th, 2021 AT 6:45 AM