boosting 3.7V to 12V
The thing you need to consider before going further is the current draw from the source. At 12V and 300mA, assuming 90% efficiency, which is probably generous, you're looking at 1.08A draw. Depending on your battery, that may not work for you. That is probably why the LT1303 didn't do what you wanted. We need to know more about the battery to say for sure, and for good measure, please post your schematic.

And if you choose to go with the MCP34063A anyway, the 1.5A "Current Output Rating" is exactly what it says it is. The datasheet says output switch current up to 1.5A, your 300mA will be fine. You don't need to put these in parallel, you need a source that can source enough power. That IC looks pretty straight forward. Just make sure you go through the datasheet and do the math on the reactive components and make sure they are appropriately sized.