Can Boost programs be transferred off the tablet / phone / PC?
This should be possible. On my Android device, the Boost files are located at Android/data/com.lego.boost.boost/files. There are subdirectories there for each model (Cat, Guitar, Vernie, etc).

The CreativeCanvas directory stores the generic programs that you have created via the canvas. These are divided into themes and activities. A single activity would be stored at Android/data/com.lego.boost.boost/files/CreativeCanvas/Theme_nnnnnnnnnn/Activity_nnnnnnnnnn. That folder then contains numbered directories containing the following file structure:


Composite Blocks


{any composite blocks created}

RecordedAudio


{any audio files}

metadata.json
palette.json
program.json
Template.json
thumbnail.png


metadata.json gives you an easy way to see what project you are looking at as it shows the name:

{
  "creationDate": "2018-07-30T13:17:13",
  "modificationDate": "2018-07-30T15:55:54",
  "name": "Ragana",
  "thumbnail": "thumbnail.png",
  "paletteLevel": 2
}


It appears that the program itself is stored in program.json. That files looks like this:

{
  "mainCanvas": {
    "positionedSequences": [
      {
        "position": {
          "x": -3.49160075,
          "y": 2.56404877
        },
        "PositionedObject": {
          "instructions": [
            {
              "operation": "Start"
            }
          ]
        }
      },
      {
        "position": {
          "x": -0.637803435,
          "y": 3.23562384
        },
        "PositionedObject": {
          "instructions": [
            {
              "operation": "PlaySound",
              "literalParams": [
                2406
              ]
            },
            {
              "operation": "PlaySound",
              "literalParams": [
                1110
              ]
            },
            {
              "operation": "EncMotorSpeedDuration",
              "literalParams": [
                100.0,
                1.0
              ]
            },
            {
              "operation": "DrivebaseBothSpeedTankDuration",
              "literalParams": [
                50.0,
                50.0,
                1.0
              ]
            },
            {
              "operation": "DrivebaseBothSpeedTankDuration",
              "literalParams": [
                -49.0,
                -50.0,
                1.0
              ]
            },
            {
              "operation": "DrivebaseBothSpeedTankDuration",
              "literalParams": [
                -26.0,
                -50.0,
                1.0
              ]
            },
            {
              "operation": "/Generic/Wait/WaitForColor",
              "literalParams": [
                9.0
              ]
            }
          ]
        }
      },
      {
        "position": {
          "x": -2.94540381,
          "y": 0.827951133
        },
        "PositionedObject": {
          "instructions": [
            {
              "operation": "/Generic/Trigger/TriggerOnColor",
              "literalParams": [
                1
              ]
            },
            {
              "operation": "DrivebaseBothSpeedTankDuration",
              "literalParams": [
                50.0,
                50.0,
                1.0
              ]
            },
            {
              "operation": "DrivebaseBothSpeedTankDuration",
              "literalParams": [
                -48.0,
                -53.0,
                1.0
              ]
            }
          ]
        }
      },
      {
        "position": {
          "x": 3.88817477,
          "y": 1.29482651
        },
        "PositionedObject": {
          "instructions": [
            {
              "operation": "/Generic/Trigger/TriggerOnOrientation",
              "literalParams": [
                2
              ]
            },
            {
              "operation": "EncMotorSpeedDuration",
              "literalParams": [
                50.0,
                1.0
              ]
            }
          ]
        }
      },
      {
        "position": {
          "x": 3.715327,
          "y": -0.0692780837
        },
        "PositionedObject": {
          "instructions": [
            {
              "operation": "/Generic/Trigger/TriggerOnOrientation",
              "literalParams": [
                0.0
              ]
            }
          ]
        }
      }
    ],
    "positionedDataBlocks": [],
    "viewState": {
      "position": {
        "x": 2.3166585,
        "y": 1.16671765
      },
      "scale": 4.0
    }
  }
}


These are simply JSON files, so you can certainly commit them to version control.

I have confirmed that copying program.json from one activity to another effectively clones the activity program. This worked for me for a basic program, but I assume you'll want the entire project structure in version control to catch more complex programs with composite blocks or other things.

There is an analogous  path on Windows with these files in it at C:\Users\username\AppData\Local\Packages\TheLEGOGroup.LEGOBOOST_m36angppq0g76\LocalState\CreativeCanvas\Theme_nnnnnn\Activity_nnn\nnn.

I'm also not familiar with any tools yet to automate this sort of thing, but it seems like they could be created fairly easily.