Plaintext Modulo Switching BFV

In my current use case, I have many binary vectors. In the context of BFV, I want to use each ciphertext to represent one binary vector. On these binary vectors, I need to do a large number of homomorphic multiplications (the multiplicative depth is very low though, like 2-4).

After those multiplications, I need to multiply each vector with a plaintext of integers, that are in a much larger modulo Q.

Thus, I would like to represent the binary vectors using a BFV ciphertext with plaintext modulo P=2, and after all computation on them is done, switch the plaintext modulo to Q and continue with some cheap computation.
I hope, that since the expensive part of the computation is done in a lower plaintext modulo, it can be completed much more quickly.

Is there any way to do this? I am relatively new to FHE, so feel free to keep your answers as thorough as possible or include links for further reading; that would be very appreciated!

Switching from one plaintext modulus to another typically requires bootstrapping, which is very expensive for BFV (the bootstrapping is not currently supported for BFV in OpenFHE).