To "move forward" means 'to continue.' "All that" in this context means 'everything (that was previously mentioned).' "with that in mind" is a phrase that means 'with that in consideration' (”〇〇をよく考えながら/考慮しながら”こと). So a rewriting of the sentence could be "while considering everything (that was previously mentioned), we're going to try to continue."

Two interpretations, #1 is more literal than #2. American English can be very indirect about the speaker's wishes or real intentions. 1) We are going to attempt to make progress on this project, and we will consider this new information. 2) We are continuing this project, and we may or may not consider this new information as we continue. "move forward"= to make progress, continue a process "with all of that in mind"= to remember/consider new information or context.