There is a newish emerging area, `applied algebraic topology'. It includes Topological Data Analysis (see work by Gunnar Carlsson and others). There is also new work again in Applied Algebraic Topology looking at Configuration spaces and probablity theory. Look for research assistant jobs at Post Doc level on specific topics in applied geometry and topology.
There is also an ESF programme (http://acat.lix.polytechnique.fr/) that gives some idea of what may be available. Some of this would provide a half way house between where you are and where you want to be! Good Luck. (Soon there is s summer school in Slovenia on these areas. Look at the program schedule and you may get some ideas on who to contact to see what they think, whetehr there are any positions coming up, short visits are a good way to start if they have money for such and seem interested. I think there is quite a good chance and all of this area is growing fast so it could be very interesting to get into it at the moment. (The topic of big data is even hitting the newspapers, and that forms part of this.)