dealing with Huge Length (Order) FIR filters
There are three different implementations of FIR filters that I am aware of.

The first is the basic "transversal" FIR in which you sum up the terms of the summation directly. It gets very expensive if $L$, the FIR length, gets long.

The second is the so-called "fast convolution" in which the FIR impulse response is zero-padded to a longer length and the DFT is applied to it once. Then there are two slightly different procedures, "overlap-add" (OLA) or "overlap-save" (OLS, sometimes called "overlap-scrap" which I think is more descriptive) to process blocks of the input into blocks of the output.

Both of these methods are well covered in textbooks.

A third method, not really covered in textbooks at all, is the "Truncated IIR" filters (TIIR) and this might apply in your case.  The simplest example of a TIIR filter is the moving-sum or moving-average that you might find in cascade-integrate-comb (CIC) filters. They have recursion in them, but they are not, mathematically, IIR. Their IIR impulse response gets cancelled or truncated.

If you're trying to implement a long FIR that is a sliding rectangular window (that's a moving sum) or a sliding Hann window or sliding Hamming window, you can do that very efficiently with a TIIR.  A sliding Blackman is a little harder and I don't think TIIR will work for a sliding Kaiser.

I have to go now, but I will return with some references. Or send me an email (it's easy to find) and I will send you copies of the references I have including a "how-to" paper I wrote about how to do biquad TIIR filters in general.