Flushbottom columns when \parskip has no stretchable glue

Question

In the following example, the columns on page 1 and 3 "sit" perfectly on the frame, while on page 2 (with the large float) the columns end a bit above the frame. Does anyone have an idea what I could do to get around the problem? (If a perfect solution is not possible, then a difference of 1-2pt would be acceptable).

Using a \parskip with stretchable part helps naturally but is not what I'm looking for. Setting \dbltextfloatsep to a specific value helps, too (in this case to 24.8pt), but it's dependent on the size of the figure and it is tiresome to find the "correct" value.

\documentclass[a4paper,twocolumn]{book}
\usepackage{lipsum}
\usepackage[showframe,
           textheight=\dimexpr\topskip+45\baselineskip\relax]{geometry}
%\parskip=0pt plus 1pt
\parskip=0pt 

%\dbltextfloatsep=24.8pt

\begin{document}
\begin{figure*}
\rule{\textwidth}{5cm}
\caption{blub}
\end{figure*}

\lipsum \lipsum
\end{document}

Answer 1

As David Carlisle explains in his comment, the \dbltextfloatsep glue is emitted in a place where it can't stretch or shrink.

I've got the correct height by loading the figure, typesetting it for getting its height and inserting a skip for compensating the difference to a whole number of lines.

\documentclass[a4paper,twocolumn,draft]{book}
\usepackage{lipsum}
\usepackage[showframe,lines=46]{geometry}
\usepackage{environ}
\makeatletter
\NewEnviron{Figure}{%
  \setbox0=\vbox{\hsize=\textwidth
    \def\refstepcounter##1{}\def\label##1{}
    \def\@captype{figure}
    \BODY
  }
  \dimen0=\dimexpr\ht0+\dbltextfloatsep\relax
  \count255=\dimen0
  \divide\count255\baselineskip
  \dimen0=\dimexpr\numexpr(1+\count255)\baselineskip-\dbltextfloatsep-\ht0\relax
  \begin{figure*}
  \BODY
  \vskip\dimen0
  \end{figure*}
}

\parskip=0pt 
%\dbltextfloatsep=20pt % set at pleasure


\begin{document}

\lipsum[1-5]

\begin{Figure}
\centering
\rule{\textwidth}{5cm}

\caption{blub}
\end{Figure}

\lipsum[6-7]\lipsum\lipsum
\end{document}