Hah, oh boy can I help you 🙂
I and my manager each completed this arduous process earlier this week as we both have 2 dogs to move from houses on the West Coast.
First I must say the airlines are VERY inconsistent depending on who you get on the phone when. Also you need to understand the difference between shipping your dog cargo vs. baggage. If you are flying with your pet you should plan to ship them baggage and given the summer and depending on the airline this may be the only option (American didn't seem to be nearly as flexible as Delta.)
In my case I booked a red-eye flight from the West Coast (actually I left in the afternoon from Seattle and red-eye from LAX) that flew straight into San Juan. However even up to the time I hopped on the flight in Seattle I was under the impression that I could not fly into St. Croix due to the heat issue. Instead I had planned to land in San Juan or St. Thomas as my destination and then take a taxi with luggage and dogs in tow over to Seaborne Airlines (www.seaborneairlines.com.) Seaborne turned out to be fantastic extremely accomodating people to work with. They will charge something silly and small like $35 for a large kennel and $10 for a small one in addition to your ticket 🙂 I don't recall their size restriction but it was either a 400 or 500 series kennel (American Eagle flights are restricted to a 400 series kennel in size.) In short you can save a bundle and not charter a plane.
If you take your dogs as luggage on Seaborne they and your excess luggage go on a space available basis. Just make sure you're not getting the last flight of the day and you are probably OK. Alternately if things get worrisome you can always buy a seat for your pet on Seaborne. Call Ms. Kareema Smith of Seaborne at 1-340-773-5991 and let her know the situation and she will take complete care of you.
Now in my case I had a problem with my checked luggage (TSA rifled through the moving boxes and one of them had been crushed and broke open) and had to get off the plane for 24 hours at LAX (had to wait to catch the same red-eye flight.) It was only when I went to rebook my next leg to St. Thomas that I learned that I could fly direct from LAX to San Juan and then on to St. Croix all on AA/Eagle because I was on flights early enough that the projected temperatures would not be too high. In the end I didn't fly Seaborne but my manager did which worked out well.
p.s. - I didn't realize I was booked on an Alaska Airlines code-share flight until I got to Seatac airport. After I checked in at LAX American tried to charge me for the dogs again because they couldn't see the payment I made in Seattle in their system. Make sure you get a receipt for any all fees along the way.
Hope this helps.