Should I go visit him first?

I would not go see him becasue he may get in the thought that you don't mind going to him. And you may not mind it but I am sure you don't want to be the only traveler. I think you should wait and give him time to think if he wants you. If you let him think that you will run to him then he will think that he can sit back and not realy try. Like you said you want him to pursue too. Kepp talking to him on the phone but I would not go visit him. If he really likes you he will not be able to wait to scome see you in september, which is only a couple weeks away. Hope I helped.

I would make sure that he has free time before you plan a trip. You said that he is busy with a project, so you want to be sure he can provide you with his full attention during the visit. Once you confirm this then I would say go for it. He did invite you and you do want to show your active interest as well. You can still let him be the pursuer, but I think it will take some stress off him if you show an active interest in him as well.