Ultimately you are talking about buying and selling so it is a negotiation and as horrible as it sounds negotiations are not normally fair.
You had a verbal agreement of 20% assuming all parties still agree thats the case use that as the base line but modify to take in other factors.
He is not really obligated to move from that point, the fact you want him out means you presumably have had a breakdown in communication the fact he worked solidly on the project without pay from the sounds of things means unless you come to an agreement that he feels is reasonable and is looked over by a lawyer you will be looking over your shoulder when you do get funding for a law suit.
From an outsiders perspective and without knowing (and I don't want to know) why you wish to fire him he holds a lot of cards. Come time to fund, you will have to disclose the partner you fired the reasons why and the settlement in detail. Investors don't like the idea someone other then the founders may have any claim to the project.
Ultimately you need to sit down and talk to your partner, but someone who has worked 100% for a year on a project when others did far less is going to believe they are entitled to a decent return now and if the company is a success. If you want to close this chapter you have to take into account his feelings and needs now, and take steps to limit liabilities in the future. You may find asking him to stay a lot easier perhaps in a different role and let him naturally drift away making the negotiations totally different.