Do you think it's possible for me to be able to speak it functionally by this June?
FYI this is an extremely difficult question to answer. You have to consider how quickly you pick up the language, how much time you spend daily actually speaking the language around other Japanese speaker's, particularly native Japanese speakers, how much vocabulary you learn and can functionally use, and not to mention whether or not what you are saying is intelligible or not.
Learning Japanese in a classroom and actually using it on the streets are two different things altogether. You learn many times text book Japanese in the classroom yet no one speaks textbook Japanese on the street. You really need to focus time on hearing and being able to understand and comprehend what is being said.
There are so many variables to evaluating whether you could be functional or not, also what exactly is your definition of functional too.
The organizers were also unclear about the costs, claiming only that we'll have to pay a "GREAT DEAL LESS than similar programs". Does anyone have any idea what the costs are for similar programs? I have some money saved up, but I planned on spending quite a bit of it. I just want to know if I have enough now or I'll need more.
This is hard to answer as well, your question is very vague. Each persons spending habits are different and it's impossible to read you mind to know exactly what you are thinking. Since many of us already live here in Japan it's going to take someone who has gone through a program like yours to respond to get an idea of what "GREAT DEAL LESS" actually is.
You could help by telling what your expected costs are, it's too vague as it sits right now. See you might be a person that likes to go out and eat and drink a lot, that costs money. Or maybe shop? Not free either. Your questions are too open ended to give any type of specific advice and sharing more information would help greatly.
You also only say over the summer, is that for 3 months? How long? Specifics please.