There are a number of great ticket systems as well as invoicing/payment systems that would make life a bit easier for you. 

and he has misspelled BOTH of our names on the invoice (mental issues?).  

If so, there's no real question here, you write them up a checkout invoice, and keep the security deposit. 

So far I’ve paid my GC every week, with his invoice including his overhead and taxes.

As (If) you get more serious into it, I would then also request to view the current Leases and well as the ones prior, the Tenant background verifications/applications and the any receipts/invoices that the current owner has paid for maintenance/upkeep (such as the new roof) during the inspection period, you could possibly use that in your favor during negotiations.

I'm honestly really fed up with the general contractor.As a reminder, I pay the exact invoices that are submitted to the GC.

If the owner(s) recklessly borrowed and lost money, made business deals knowing the business couldn't pay the invoices, or otherwise acted recklessly or dishonestly, a court could find financial fraud was perpetrated and that the limited liability protection shouldn't apply.https://www.nolo.com/legal-encyclopedia/personal-liability-piercing-corporate-veil-33006.html

Ask to see payment history of existing tenant and any invoices/payments to contractors.

I think that showing them these things helps them to better take care of the property, and helps to reduce potential damage if a pipe breaksI schedule showings 15 minutes apartI waste less time driving to and from the property, and between applicantsThey see other applicants arriving or leaving, so they know there are others interestedI ask them to call to confirm at a specific time a few hours before their appointmentI don't have as many no-shows (believe it or not, there are still no-shows even when they called 1/2 hour earlier to confirm)I print our standards on the application (600 min credit score, 3x rent as income, no smokers, we do background checks, etc)Allows applicants to decide if they want to weed themselves outI encourage applicants to take the application home to fill it outI offer to pick it up at their home so I can see how they liveIt requires them to follow up and return it if they're interested, so I don't have to screen through people who apply everywhere with the shotgun approachIf they insist on filling it out on the spot, I call to confirm a fact from their application before further screening to make sure they're still interestedWhen they turn in their application, I tell them I'll be conducting background checks and ask if they have any surprises I'll hear about that they want to discuss.They've often told me about things that didn't appear on the reportThey've asked for the application back, said they wouldn't qualify if I'm going to do a background checkAll of my units have pass-through knobs and deadboltsThe tenant has to actively lock the door behind themThey can't lock themselves out by pulling the door shut behind themselvesAll of my units have been changed over to a master key systemI have one key that unlocks every door that I own, including padlocksInstead of replacing the whole deadbolt, I can swap out the core in 30 secondsNo more softball of keysI have a lock core in a different color that I can put on vacant units that are being worked on so I can give contractors a keyI have a standard set of 4 colors that I paint every unitIt makes it feel more like home if the walls aren't stark whiteIt doesn't cost anything extra to paint rooms different colorsThey're all earth tone colors that go with any furnitureWhen tenants ask if they can paint their unit, I tell them yes, but here are my standard colorsI've eliminated carpet - I use tile, snap-together vinyl laminate, concrete, hardwood (if it's existing) or linoleum (rarely)Tenant can bring their own throw rugs if they wantReduces allergensEasier to cleanI don't use the old snap-together pressboard laminate that would curl up with moistureI pay contractors as soon as I receive an invoice and I know the work is done to my satisfactionContractors don't want to chase down customers any more than we want to chase down tenantsI get a quick response in an emergency because they know I'm going to pay right awayI never say "no" - I always give them an option of how to get it donePets are okay, but there's a monthly feeIf a pet is sneaked in, there's a fine plus the monthly feeIf a pet is deemed dangerous to the property or neighbors, they can get rid of the pet or move outIf you're caught smoking, there's a large cleanup feeIf they want to paint, I let them choose from my colorsIf they're going to be late, the late fees are clearly definedIf they want to move in another roommate, that person has to apply and be qualifiedIf they want to move because they need more space, they can move into one of my larger units without breaking the leaseIf they don't mow the lawn or clear the snow, we can arrange to have a service take care of it at an additional chargeI'm sure there are other things I've added to my toolbox over the years, but this is a good list to start. 

Now he has sent me an invoice charging me for things I have already paid for and he refuses to meet with me to discuss.