It's hard to predict what bases are available for new hires at any particular time- CMH and LAX have been the hardest for them to fill so far (they didn't hire into the others for many months), but they have recently been hiring into all of the bases. Home basing is not probable for any new hire for the duration of the current contract since you need to be in the top 30% (excluding those who are already living in the 5 domiciles hired precontract). This is unlikely in the 5 years of this contract, unless they have a hard time attracting quality applicants (also not likely). Switching to NJI is probably also very unlikely since you will need to be here for 2 years before you can go and in a little over 2 years from now they have to figure out how/ if there will be integration between NJI and NJA.
If you tell them you are willing to live in any domicile and get hired quickly, you can change domiciles within the 5 as long as a position opens up or someone will swap with you. There is a possibility that more domiciles or widespread homebasing will come before the end of the contract, but I wouldn't bet on it. It is a very good job, but to take it you better be willing to live in or within driving distance of one of the 5 domiciles for at least as long as it takes to get a new contract. There are new hires driving 6 hours to get to domiciles and some paying their own way for airline tickets (can add up very fast). I moved to my domicile and I'm willing to accept it until I have more living options because I think it is the best job for me. I don't like any of the domiciles, but I know some time I'll have more options and it is well worth it to me to sacrifice now for a better future. Good luck whatever you decide.