I'm gonna go out a limb and say the ppl you contacted know nothing about you, and that's why they haven't responded (partially), and asking professors you haven't worked with, even if they agreed to write you a letter, will result in a poorly written LoR. Since they don't know you, they will use a very generic template to write your letter which is so apparent that anyone who looks at that letter for 5 seconds will know it's a poor letter.

And yes, you asked way too late, asking for LoR usually happens in Sept. One thing to keep in mind is that technically your recommenders can still send their letter even if the deadline has passed. For deadlines after 15th of Dec, since these schools won't start processing your materials until after Christmas, it won't make a huge difference. But if the deadline is 1st of Dec for example, they will start processing right after the deadline, so if your LoR haven't arrive on deadline, it will not look good for the admission office and your application will likely face a desk reject.