The Great Planes Electrifly Rimfire 28-22-1380 is a great choice for a brushless upgrade for a brushed speed 180 and it's only $24.99. You can use most any 10A brushless speed controller you'd like. E-Flight makes a nice one with a JST connector for the battery and 2mm female bullet connectors that will match up nicely to the 2mm male bullet connectors on the Rimfire 28-22-1380. The E-Flight 10A brushless ESC runs about $27.99

Your 1200Mah 7.4v LiPo cell will run forever on this power combo, in fact, a 640Mah battery would give very long flight times. If you try to fly it with the 1200Mah battery, you'll likely want an adapter cable so you can connect it to the JST connector on the speed controller. You might consider spending $20 or so for a 640Mah 7.4v LiPo to reduce weight.

As for screwing the engine directly to the firewall, you would probably be better off buying the Electrifly GPMG1250 small electric motor mount. At $14.99, it's almost as much as the motor, but it will allow you to better position the motor out away from the firewall so you can fit the cowling over it for final flight.

Good luck, and post some pictures of your new brushless Jenny!