Many older and lower-tiered Canon bodies such as the Rebel SL1/100D and T2i/550 do not have user selectable options for AF priority. With default menu items selected:

• 'One-Shot AF' is always focus priority
• 'AI Servo AF' is always release priority

On advanced Canon bodies it is usually under one of the multiple AF tabs in the main menu. With the 5D mark III and 7D Mark II, for instance:

• 'AI Servo 1st image priority' is the first menu item under the second 'AF' menu tab
• 'AI Servo 2nd image priority' is the second menu item under the second 'AF' menu tab. (This applies to the second and all succeeding images in a continuous burst)
• 'One-Shot AF release priority' is the third menu item under the third 'AF' menu tab

Per Chuck Westfall, the head of Canon USA's Professional Client Relations Division and former Canon Technical Advisor:

AI Servo AF allows photographers to release the shutter at will, regardless of whether focusing has been completed or not. This is intentional, in order to allow the photographer to prioritize capturing the peak moment regardless of focusing status. The trade-off is the fact that there is no guarantee that the focus will be sharp on a stationary subject in AI Servo AF, especially during handheld photography at close range with shallow depth of field. Under these specific conditions (one more time for emphasis, I am saying Stationary Subject, handheld photography at close range with shallow depth of field), One-Shot AF is a more reliable focusing method because it locks focus while AI Servo does not.

When the shutter button is pressed all the way in AI Servo the camera fires whether focus has been achieved or not.

For more on the differences between 'One-Shot AF' and 'AI Servo AF', please see: Is there any reason you would use one-shot focus over AI-Servo?

Other Options

I do not want a "work around", such as switching between AF and MF, as suggested by Canon EOS 400D - Shutter Release Lock Override.

I'm not sure if you consider this falling within the comment above, but there is a way to turn AF 'On' and 'Off' without using the switch on the lens.

If your cameras have a menu option to use back-button AF without the shutter half press activating AF, then AF is 'On' when the back button is pressed and 'Off' when the back button is not pressed. Likewise, if a back button is set to be 'AF Off', then pressing it should allow the shutter to release without having the camera confirm AF.

With the Rebel SL1/100D (The Rebel T2i/550D should be similar), the 'Exposure Lock' or 'AE Lock' button (the button marked with a six point asterisk that doesn't show up when we type it into the body of an answer here) can be remapped to serve as an 'AF-On' or 'AF-Off' button. It's covered on page 303 of the Canon EOS Rebel SL1/100D Instruction Manual:

When Canon includes a slash (/) in the header of an option with the name of one button to the left of the slash and another button to the right of the slash, the descriptions in the options below it indicate that everything to the left of the slash is assigned to the first button, and everything to the right of the slash is assigned to the second button.

If using [option 1: AE Lock/AF] the shutter button half press only performs AE lock and the 'AE Lock' button on the back of the camera turns AF 'On'. Releasing the 'AE Lock' button turns AF 'Off'. When AF is 'Off', the shutter should fire without the camera confirming AF. This allows 'shutter release priority' in 'One-Shot AF' mode. It does not allow the user to select 'focus priority' in 'AI Servo AF' mode, however.

If using [option 2: AF/AF lock, no AE lock] the shutter button half press initiates AF and the 'AE Lock' button on the back of the camera turns AF 'Off' (by locking the focus mechanism at the then current position) when it is pressed. Exposure is not locked until the shutter button is fully pressed. This should allow 'shutter release priority in either 'One-Shot AF' or 'AI Servo AF' by pressing the 'AE lock' button. As with option 1, there's still no way to set AF priority in 'AI Servo AF' mode.

Option 3 is like option 1 except exposure is not locked with the shutter half press, but is set when the shutter is fully pressed.

"FujiFilm release priority: focus far, point at near subject, press shutter ⇒ focuses (tiny fraction of second), fires shutter."

For what you want, set C.Fn-6 to option [2: AF/AF lock] and use 'One-Shot AF' mode. When you press the shutter button the camera will focus before firing. If you want the camera to go ahead and fire, press the 'AE Lock' button on the back that has been remapped to 'AF Lock'. The camera will fire immediately.