- acquire a GPS signal very quickly (within ~10 sec) upon initial power-up regardless from when it was last powered up (thus, hot-start capable with the use of a coin battery perhaps)
Not possible. The satellite's orbits are constantly changing, so the battery backed data are good for only a period of time. The data rate from the satellites is very low (takes several minutes for a complete almanac message to be sent) and if the GPS unit doesn't already have a good idea which satellites are in the sky, it has to wait until enough have been completely identified and accurately located before calculating the position. You may have to wait up to 15 minutes for a completely cold "factory" start. Time to first fix - Wikipedia
Edit: Of the many I've used, I'm happy with the following battery backed Locosys module, which in the best case can get a fix in well under 10 seconds after turn on. It does not have an external antenna connector: http://www.pololu.com/product/2138