Given sentence 'Dogs are my choice', can I use singular verb form for any reason?
You can "justify" the singular verb form Dogs is my choice on the grounds that my choice is singular, or by appeal to the use–mention distinction (the reference is to dogs as a single token, not to the plurality of animals represented by that token).
It's not really any different than Fish and chips was my choice in the restaurant or When it comes to sexual preference, my choice is women. As a general tendency, BrE is more flexible in this area than AmE, in that we're more likely to ignore strict logic/grammar, to reflect the semantics of an utterance.
I don't have any problem with...
...after which the following conversation could ensue...
Speaker B: You said "cats and dogs", but I only like dogs, not cats. What should I say my choice is?
Speaker A: Just say "My choice is dogs". Only a misguided pedant would argue with that!
Speaker B: Okay, but can I reorder that to "Dogs is my choice" if I want?
Speaker A: Sure. But even some people who aren't particularly pedantic might not like it much