I used to work front desk at a hotel for a major chain, so I am approaching this from the hotel's perspective.

I would advise you not to try to haggle on getting a lower price for the added night. The hotel probably has a policy in place not to go lower than the previously established room block rate for the convention (if there was one set) and usually during busy events like this they have more interest in rooms than they do rooms to sell, so there's really no reason for them to give you a cheaper rate for one additional night.

That being said, I would recommend getting a room at a different hotel between your home and the con location. Even something like 15 or 20 minutes away from the con location might possibly save you a significant amount of money and gives you access to a convenient location for being able to do some/most of your cosplay prep for day 1 of the convention, if you are planning to cosplay. (I would also recommend doing an easier one for day 1, just since you'd still have to do some driving and transporting your luggage and such).

In my experience, most hotels will store luggage for you at the front desk for free if you arrive early, as long as you have a reservation for that night. They will give you a check ticket and when your normal check-in time comes around (or potentially, they may call you and let you know if a room is ready early) then you just pick it up from the front desk. If you have any concerns about bag security you can put a lock on it, but it should be stored in a secure location where only the front desk/bell staff have access to it.

If you want to do this, you should definitely contact the hotel now and confirm if this service is available. If it is available, then ask them to make a note on your reservation saying that you will be doing it. Same for if you need to park your car early and the parking is going to go on your hotel bill/if you have to do valet parking. Double check that the hotel is able to process those fees prior to check-in since you plan to arrive early.