I'd suggest going for a dedicated Yagi or similar directional antenna tuned specifically for 2.4GHz with the right connector for your transmitter. L-Com has gear that I have had good luck with. Hopefully, the high gain of the directional antenna can help 'burn through' the non-LOS component of the transmission.
A high-gain antenna will limit the area a bit where you can receive, but as long as it's not too high a gain, you will get a pretty wide 'cone' that you can receive within. For example, the 9dbi gain YAGI they offer http://www.l-com.com/productfamily.aspx?id=6310
offers a 60 degree-wide cone in the horizontal as well as the vertical axis. For $36 it's a pretty good deal and you may even be able to order one with your specific connector on it (not sure what the SMIRF uses).That would eliminate a connection (with the attendant 0.1db loss of signal) and a failure point.
Another option is using a 2.4GHz amplifier - expensive, needs power, etc. but you can put out up to a Watt of power...
Another option is to put in a long-distance system at the weather station to get to a fixed point within the house, then install a bluetooth re-transmitter there. For example, the http://iteadstudio.com/store/index.php?main_page=product_info&cPath=7&products_id=127
allegedly features a 2km range. Your baud rates are sufficiently low that the whole thing may just work.
Last but not least, see if your transmission issues may be related to the use of Wifi in your home. Given the very low power output that Bluetooth transmitters typically operate with, your Wifi computer network, (or worse yet) wireless telephone transmissions may be 'stomping on' and disrupting your Bluetooth transmissions. It's one reason why I have 5.8GHz phones in my house - it keeps the Wifi system happy.