It's either one or the other, you can't have BTWEA on JB, if you go for the STEA while on JB it's really just a change of name, you only get the benefit until the original JB claim would have run out anyway.
The BTWEA is a longer payment as you say and only for people who have already been on benefits for 12 months, I thought you had to be on JA for 12 months, maybe it is just 12 months in total on JB/JA? What's the technical allowance?
Will you qualify for JA when your JB runs out? The 40k exemption from tax would big a big carrot if you expect to make money in your first few years.