Is it permissible for my father to withdraw from the project and retrieve his money after its purchasing power has decreased, or should he calculate the full cost of the project and take a profit proportionate to the amount he paid, instead of splitting it fifty-fifty, especially given his rejection of the idea of loans to complete the project?

Your father is not forbidden from remaining in the project, because the prohibition of an interest-based loan is related to the liability of its recipient, not to the specific item it was used for. However, it is preferable not to associate with someone who deals in usury or does not avoid forbidden things. There is no objection to your father selling his share to your uncle for any price they agree upon. If they desire the true value, it is the market price on the day of sale.