When five or more people tell you “danger, don’t do it” about something, you’d better take them at their word.
Your choices are to turn the clients down politely but flatly, counter-offer a way to do it that fits their stated budget, (IF you are personally willing to work on it that way,) or refer them to your competitor.
That last trick will either saddle the competitor with a money-losing, time-eating job, or he will try to lowball it, and the resulting train wreck will send your now-humbled clients back to you, their savior, who, regrettably, must charge even more now to fix the lowball project.
Finally, you would be surprised at the number of hard-limit figures that suddenly magically get revised upwards after you’ve turned them down flat and let them stew in their own juices for a couple days. Their deadlines need not be your deadlines unless you sign on, and remember that as the clock ticks down on their deadline, they are sweating way more bullets than you. They still have a boss to please, even if you’re not taking their assignment. Likewise, maybe it’s better for everyone if they hold off doing something overly ambitious until they can afford to do it RIGHT.
A couple times early in my career, when I was more foolish/fearless/candid and had nobody else to support, I flat out told a few potential clients that their project was a waste of money and time because it was not something that could be helped by making a video, at least, not the kind of video they were asking ME for. I said I would be ashamed to take their money and not deliver something that would actually help them, and that I’d rather have their respect for saying no on principles than their money for being a yes man. Then I lef tthem with a couple of heartfelt suggestions as to alternative methods that would be a better fit for their needs.
A couple times that turned out exactly right, and it was because I had NOT caved in and done a half-fast job before, that they came to me again later to make something “done right”.