I am sorry you are having some trouble with your new rescue Staffy X Mastiff. That doesn’t sound like much fun at all…
Good on you for looking into veterinary behaviourists! I can appreciate that costs can be a limiting factor. Chatting to your local vet in more detail would also be a good idea. I am not sure who you have rescued him from, but it may be worth giving them a call to discuss any concerns you are having. I suspect they would be more than willing to offer some assistance to ensure you have a healthy and happy relationship with your new little mate.
He is still very young so definitely training him to understand that mouthing is unacceptable is important. If he goes to nip/mouth you vocalise “Uh uh!” remove your hand and replace it with a toy he is allowed to chew on and give him lots of praise for chewing the toy. This is the first step in teaching him what he is allowed to chew and what he is not. This requires lots of repetition and consistency and will not change overnight. Focus on positive reinforcement for doing what you want him to do, rather than punishing him for what you don’t want him to do.
Taking him to obedience training would also be a good idea. Ensuring he is getting lots of exercise and play time (fetch, tug) is really valuable because he is a very active dog. This will help him feel more calm and content. It might be worth keeping him confined into a certain area of the house, using child safety gates for example, when people are visiting. Taking him for a long run somewhere fun before people visit should also help him feel more settled.
I hope this has helped! If you are still having trouble seeing your local vet to discuss his behaviour and routine in more detail would be helpful to understand why he is behaving this way. He may need medical help for underlying anxiety if this is present so they will be able to help you with this.
Best wishes to you and your darling rescue! I look forward to hearing how you get on.