airlines taking dogs in baggage from US to Punta Cana

I appreciate any actual, fairly current feedback here.  We have a Corgi who always flies in a kennel with baggage.  He is too big for the cabin, and he is not a service animal.  My wife and I and our dog are planning to live in Punta Cana area this coming winter.  Our plan is to fly from Portland, Or. to somewhere East Coast or South on Alaska (who always take good care of our dog).  However, it is from that arrival point we are having difficulty planning the remainder of our trip.  I have researched about 20 different airlines who fly to/from Punta Cana.  I am down to maybe American Air, United and maybe Frontier.  There may be others I have missed.

We have lots of time, but we are going to have to deposit funds soon for our rental (already reserved for us) in the next few months.  Who has flown their dog from the US non-stop to Punta Cana in the baggage compartment lately?

Some airlines do not allow dogs in baggage on certain types of aircraft (alaska included), some airlines do not fly during the hours it is cooler to Punta Cana, so there lies the problem.  Please, if you have specific cities, airports, airlines etc. who can get us there from the US, share any details. 

We have travelled to Mexico many times with our dog, so we are familiar with the legal stuff, vet stuff, crate issues etc...no problema!  We just need some guidance.  Please includes most recent date for your travels, so we can look at potential options.  Our travel dates are flexible.  We prefer early November coming in, and sometime April going out of DR. 

Thank you very much.