awk – Joining multiple lines based on a regex

I have the output of a pandoc conversion to HTML which looks like this:

foo

bar

<blockquote>

That's one small step for man, one giant leap for mankind

A new line and another quote

</blockquote>

baz

I’d like to make it like this:

foo

bar<blockquote>That's one small step for man, one giant leap for mankind

A new line and another quote</blockquote>baz

(Because block quotes are rendered separately anyway so I don’t need the extra new lines.)

I started trying with sed and ended up with this awk:

'/./ {printf "%s%s", $0, ($1 ~ /^$/ && $2 ~ /<\/?blockquote>/) ? OFS : ORS}'

Which does part of what I want, but is a bit too advanced for me to understand how to modify.

In words I think the rule I want is: if the next line is blank and the one after matches /<\/?blockquote>/, then print current line, next line, and the one after without any separators, and then move on.