If you right click on the game page and select 'inspect' you can open up the console window. Find the Application tab and under localStorage find the thing labeled something like game324380. You can delete the GameRecords file and it will reset your records. This is for Chrome but other browsers should be pretty similar.
I had an interesting idea. What if there was a mode where you had to use all the heroes at once? That would make for a unique and cool gameplay granted you can iron out the balancing issues which it could bestow. Food for thought.
If you right click on the game page and select 'inspect' you can open up the console window. Find the Application tab and under localStorage find the thing labeled something like game324380. You can delete the GameRecords file and it will reset your records. This is for Chrome but other browsers should be pretty similar.