We are in a similarish situation. We sold our home, increased mortgage to buy another, but decided to keep the property we rent out. We realised that it will be so much harder to get back into renting in the future if we ever wanted to with stamp duty changes etc. Plus it will give us a great nest egg when we come to retire (either by selling it or continuing to rent it out). We use an agency which takes away a lot of the stress of tenants.
We both also made a decision we would not want to evict our tenant to sell (rather wait until they decided to move on) but obviously that is a our personal view.
I think plan D makes sense. BTL mortgage rates are high and so are the initial costs so I'd pay that one off but have a higher residential mortgage on the new place as the interest rates are lower. That could increase your income tax but would be easily offset with higher pension contributions. I'd be reluctant to take out 3 mortgages as the rates are only going one way + it can all be stressful.
Not Plan C unless you have a huge amount of savings. If you get a tenant who doesn't pay their rent, it can take months to get rid of them. Unless you can cover all the mortgages without the rental income, you could be putting your own home on the line.
If you're renting a place, you need a BTL mortgage. If you have a residential mortgage on a rented flat, you need permission from your bank or a buy to let mortgage. Otherwise it's a breach of contract.