Hi,
I am currently trying to implement a transciphering scheme in the style of https://eprint.iacr.org/2020/1335.pdf using the openFHE library.
Concretely, I have to compute a symmetric keystream while performing the operations under BFV encryption, and then switch encryption scheme from BFV to CKKS. I have 3 loosely related question concerning this:

Is there an easy way to switch between BFV and CKKS? In particular, since we can set ciphertext modulus and dimension to the same value, it is in theory possible to generate a single key pair. However, it appears that the keys are signed by the cryptocontexts, making it difficult to do in practice.

The paper requires a SlotsToCoeff operation with BFV (which may be avoided a the cost of an additional encoding). A thread from a year ago mention that bootstrapping for BFV is on its way, do you know if it will appear in the near future, or should I try to find some alternative?
The thread: BGV/BFV Bootstrapping 
The process requires overall a multiplicative depth of 12 + anything needed for the CKKShomomorphic decryption of the BFV ciphertext. Is there any good choice of parameters allowing such a depth of calculation with BFV with a reasonably large PlainTextModulus?
It is very easy to hit an infinite modulus (more than 2^1024 I guess) if the parameters are chosen poorly. In particular, with ring dimension 2^16 and lambda = 128, extrapolating the homomorphic encryption standards shows that log(Q)=1600 is admissible.
Thanks a lot in advance