Alkaline AA's will deliver around 700mA before they start to get hot.
The receiver is going to be low-power, and the arduino itself doesn't take much. I think the Traco has more than enough capacity for your application.
You can use a voltage divider on the output of the transmitter to get the signal down into range for the 3.3V trinket, but you'll still need 5V for the other components.
The 5.5V requirement for the trinket is when you go through the voltage regulator. I believe that you can attach a regulated 5V supply to the USB 5V pad.
jc27 wrote:Here are the power requirements for the components so far:
Trinket 5.5-16vDC (or 3.5-16vDC for the 3.3 trinket)
315MHz receiver 4-15vDC
Given that, you don't need to use a voltage regulator at all. Each of your three components already has a voltage regulator, and all three will run from 6V.