TL;DR: "What else can you do...?" Ask admissions officers at schools you're waiting on so you might get more information. There may also be value in asking faculty you know well.
I make the assumption that faculty at that masters program would have little power/incentive to change the commitment deadline for the OP in this case; any comments with evidence for or against this assumption would be useful.
You have two pressing questions: is what they are doing ethical, and what can you do? (I now address the ethical question at the end.)
Since that program does not want to budge, you could politely inquire of one of the programs you are waiting to hear from. If you explain this situation, saying that you take a commitment to a school seriously, they may be able to address whether you still have a reasonable chance of admission to their school this year and/or whether you are likely to hear a decision by the masters program's deadline.
Because of the April 15 Resolution, the other admissions offices are probably not bombarded with these questions (I assume). An administrator would probably feel free to say that they cannot answer the question if they do not want to or cannot answer. This approach is unlikely to yield a definitive answer unless there is a yes or a no they are about to send out, but it might give you more information before you send a deposit.
If you have a good relationship with a faculty contact at a school you're waiting to hear from (e.g. a recommender or someone you have extensively talked with about potentially working with them), you could explain the situation and ask if they have any advice. You may get no response (faculty are busy), generic advice (such as you're getting on this site), or advice with inside info ("Well, you're near the top of our list..." or "This was a strong class of applicants this year, so it would take a lot of luck for this to happen..." or "We're really not sure yet what our class will look like, and we don't usually know further until much closer to April 15.").
Unless you have an extremely good relationship with a faculty contact at this unfunded masters program (for instance, they were your undergrad advisor as well), it would probably do little good to ask advice of a faculty member there. You'd be questioning your commitment to their program (which would not be a great way to start a relationship with someone there if you do attend). Faculty may have little control over the present workings of the administrative process, and/or changing the rules for you might set a precedent that harms their program.
I believe I'm in agreement with the other posters on what your course of action should be, though everyone phrases it slightly differently. If you do not have all your information, it is OK to accept the offer but back out later. It's within the school's rights to demand whatever they want, as they are not bound by the agreement for funded graduate programs, but that their demands are somewhat coercive toward someone in your position and that it would be best (though beyond what is ethically required of them) to give you more time. (Especially so because they did not make this timing conflict clear when you applied.) Given the existence of a deposit payment, you are not obligated to remain enrolled if a far more beneficial offer comes along: they have made this a financial obligation on top of/rather than one of honor. (In the U.S. mortgage crisis, the people who were worst off were those who felt morally obligated to continue payments on their "underwater" mortgages, while more financially savvy people cut their losses and walked away.)