Got to second interview. I have got concerns about notice period as I think they are trying to fill the role ASAP. But let's see.
Are your employers not flexible with it? I had a 6 month one and when I wrote my letter I put something about I understand it is 6 months but I would appreciate if my leaving date could be <less than>. I indicated to the potential new employer at the time what it officially was but that I would try and lessen.