No that is currently sadly not possible.
What you are describing are actually currently two different IDs.
One is the ID of a currently running execution. Every execution will always get one as it gets used like you already wrote to, for example, stop a running execution. This ID simply resets with each start of the n8n instance and gets incremented by 1 with every execution. This one could theoretically get exposed inside of the workflow.
A totally different ID is the one of the past saved executions. This one is only given to executions that get saved to the database. Depending on the settings that are none, the ones that failed, the ones that did succeed or none. This ID gets incremented by 1 for each saved execution and never resets (unless obviously the database gets deleted).