I don't think most program directors even know what is on their website. You are interested not on what is on the program website, but the GME (graduate medical education) website for the university/hospital. If it says 'we never ever ever ever sponsor H1B visas mutha****as' then you will know to avoid applying there. However most of the time it will say something like 'we prefer J1 visas', or 'only under exceptional circumstances'. You shouldn't bring up the visa thing in the interview, in all but one of my interviews the PD had asked about the visa thing and will usually say something like 'you don't want a J1, we'll sort you out with a H1B visa' or 'we want our residents to come and work here as attendings after residency so we would want to sponsor you for permanent residency' etc. I interviewed at a program that says on their website: 'we only sponsor J1 visas'. Which shows how clueless they are - programs NEVER sponsor J1 visas, they are sponsored by the ECFMG. Anyway, at the interview the PD asked me about my visa requirements, and I said I am on an F1 and would need a H1B visa. He said that was fine.
If a program likes you they will sponsor you for a H1B visa. If the admindroids won't allow it they will be very apologetic and say 'even though we would like to we can't'. If anyone makes an issue about it, you don't not want to go there. I would make it known, should the issue arise that I will not be ranking any programs that will not sponsor me for a H1B visa. They need to put their money where their mouth is as far as Im concerned.
It is an incredible hassle having a J1- they are 1yr only so you need to fly back to the UK and get it extended each year, you need to get a statement of need from the DoH (and who knows how long that will continue there is no need for consultants they need middle grades for rota fodder), whilst a H1B lasts 3 years, can be extended for a further 3 years, allows you to switch on to other visas, apply for permanant residency etc.
See how things go on your elective - I mean your evaluation/LoR from this elective will be extremely important in determining where you should apply. You have to remember no one will give you a bad evaluation but a good evaluation is a bad evaluation. In American satisfactory = awful, good = bad, very good = satisfactory, excellent = good, outstanding = very good, exceptional = excellent and some places even have 'superior'. So your evaluation may not be as good as you think it is compared to how it would be in the UK. Anything less than 'sineapse has performed at a level that is superior to the interns that normally staff the department' and you should start scratching your head. Also you want your supervisors to be so impressed with you they will be willing to make calls or put in a word to the programs you are applying to, to get interviews.