How to draw a conical spiral / redraw diagram?

I'm trying to redraw the diagram diagram below. I'm using it as an exemplar/reference in a document I am writing but I need it to be clearer hence the redraw.

I tried and failed to draw it in Inkscape. After thinking about it for a while though, I thought actually it could be done (and perhaps better) mathematically using something like Tikz. I've looked through the questions here and I can find similar but not what I need.

So far, my code is a just a pathetic cloud and an oval and missing the crucial 2D spiral cone:

\documentclass[]{minimal}

\usepackage{amsmath,amsfonts,amssymb}
\usepackage{tikz}
\usetikzlibrary{shapes}
\usetikzlibrary{automata,positioning}

\begin{document}
\begin{tikzpicture}
\node [cloud, draw,cloud puffs=10,cloud puff arc=120, aspect=2, inner ysep=1em,text width=1cm]{Needs\\and\\Ideas};
\draw  (0,-10) ellipse (4 and 2);
\end{tikzpicture}
\end{document}

-

You can use (point a) to [in=degree,out=degree,looseness=value] to draw bent lines. I used two sets of those, computing the coordinates in a loop. Afterwards, another loop is used to set the descriptions. This answer uses Caramdir's solution to this question.

Code

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{arrows,decorations.markings,shapes}
\renewcommand*\familydefault{\sfdefault}

\begin{document}
\begin{tikzpicture}
\foreach \x in {1,...,7}
{   \draw[decoration={markings, mark=at position 0.8+\x/60 with {\arrow{latex}}},postaction=decorate] (1+\x/5,-1-\x) to [out=90,in=90,looseness=0.5] (-1-\x/5,-1-\x) node[xshift=-0.05cm] (gate-\x) {\footnotesize stage gate};
\draw (1+\x/5,-1-\x) to [out=270,in=270,looseness=0.5] (-0.8-\x/5,-\x);
}
\foreach \gate [count=\c] in {asdf,sdfg sdfg,dfgh dfgh dfgh,fghj fghj,ghjk,hjkl hjkl hjkl,TeX TeX TeX TeX}
{ \node[text width=2cm, align=right,left=1cm] at (gate-\c) {\gate};
}
\draw (-2.4,-8) to [out=270, in =120] (-1.5,-9);

\node [cloud, draw,cloud puffs=10,cloud puff arc=120, aspect=2, inner ysep=1em,text width=1cm,fill=white]{Needs\\and\\Ideas};
\draw[fill=white]  (0,-10) ellipse (4 and 2);
\end{tikzpicture}
\end{document}


-