How do you pronounce " a "

That depends partly on the context, partly on personal preference/habit.

Speaking for myself, if I'm emphasizing the indefinite article (for instance, to inquire as to the extent of the generic nature of what I'm describing) — such as when asking for clarification, as in "Do you mean if I kiss ɛɪ frog or this frog?" — I'll tend to pronounce it as ɛɪ. Otherwise, ə would be the usual pronunciation in most other situations.

I agree with you that the divergence of the pronunciations in your example sentence seems strange — I can't seen any obvious semantic reason for it. In that sentence, I think most people would pronounce it as ə in both cases.

The most likely possibility that occurs to me is that the announcer was reading from a script without concentrating properly, and therefore inadvertently ended up stressing the first 'a' incorrectly.

(Incidentally, I have yet to unmask any princes using this method of investigation.)

It may have been only for emphasis. I've heard people do that sometimes for no obvious reason. Apart from emphasis, I would pronounce it [ei] in all situations where "a" is not an article ("good job. You guys are certainly a-team." or "He was a very bright guy. A straight a+ at high school." Also, if I had two frogs, frog A and frog B. Then I would say "kiss frog A and see what happens". (nothing, I presume)