MacOS – Shift-Option- is adding accented characters

One option would be to download changeInput and assign shortcuts to shell commands like changeInput U.S..

You could also use KeyRemap4MacBook:

<?xml version="1.0"?>
<root>
  <vkchangeinputsourcedef>
    <name>KeyCode::VK_CHANGE_INPUTSOURCE_HIRAGANA</name>
    <inputsourceid_equal>com.apple.inputmethod.Kotoeri.Japanese</inputsourceid_equal>
  </vkchangeinputsourcedef>
  <vkchangeinputsourcedef>
    <name>KeyCode::VK_CHANGE_INPUTSOURCE_KATAKANA</name>
    <inputsourceid_equal>com.apple.inputmethod.Kotoeri.Japanese.Katakana</inputsourceid_equal>
  </vkchangeinputsourcedef>
  <item>
    <name>change_inputsources</name>
    <identifier>change_inputsources</identifier>
    <autogen>__KeyToKey__ KeyCode::E, VK_CONTROL | VK_OPTION | VK_COMMAND | ModifierFlag::NONE, KeyCode::VK_CHANGE_INPUTSOURCE_ENGLISH</autogen>
    <autogen>__KeyToKey__ KeyCode::H, VK_CONTROL | VK_OPTION | VK_COMMAND | ModifierFlag::NONE, KeyCode::VK_CHANGE_INPUTSOURCE_HIRAGANA</autogen>
    <autogen>__KeyToKey__ KeyCode::K, VK_CONTROL | VK_OPTION | VK_COMMAND | ModifierFlag::NONE, KeyCode::VK_CHANGE_INPUTSOURCE_KATAKANA</autogen>
  </item>
</root>

See the private.xml documentation.

VK_CHANGE_INPUTSOURCE_ENGLISH is defined in vkchangeinputsourcedef.xml. You can see the IDs of input sources from EventViewer.app. Without | ModifierFlag::NONE for example the first setting would also apply to control-option-shift-command-E. See the source for the key code values and predefined settings.

Got this all from more recent Brett Terpstra posts, so full credit to him.

Using Karabiner Elements and BetterTouchTool, you can create a "Hyper" key mapped to control-option-shift-command (which probably won't be used by any apps as a default modifier). Then you can use BetterTouchTool to maps Cap Locks + "a" to type "=". Typing "a" by itself still gets the letter "a". You can also set it up that tapping Cap Locks alone functions as the escape key or even as standard Caps Lock.

Rather than reposting Brett's code here, I'll link to the post: A Hyper Key with Karabiner Elements, full instructions.

Some screenshots to help guide you along:

After adding Brett's code to karabiner.json, the Complex Modifications pane will look like so. No need to do anything else here.

In BetterTouchTool, switch to the Keyboard pane, add a shortcut, type Caps Lock + character, then choose "Insert/Type/Paste Custom Text" as the Trigger Predefined Action.

In the Insert/Type/Paste Custom Text sheet, type the character(s) you want and choose "Insert Text by Typing".