Thank you @duizendnegen and @Isaac Askew, observers were a great starting point and led me to the final solution. This observer code, placed in my application route, helped me figure out exactly what I could add as user context:

window.serviceState = {};
// eslint-disable-next-line
let serviceState = window.serviceState;

export default Route.extend(ApplicationRouteMixin, {
  // observes services for state changes we care about and stores them in
  // a separate variable so when an exception occurs, we can simply include that
  // variable and avoid the risk of causing another exception by trying
  // to read them in `captureException`
  serviceStateTracker: observer(
    'service1.prop1',
    'service2.propA',
    function() {
      [
        'service1.prop1',
        'service2.propA',
      ].forEach((prop) => {
        let newValue = this.get(prop);
        if (serviceState[prop] !== newValue) {
          if (serviceState[prop] === undefined) {
            console.log(prop, newValue);
          } else {
            console.log(prop, 'changed from:', serviceState[prop], 'to:', newValue);
          }
          serviceState[prop] = newValue;
        }
      });
    }
  ),

However, I did try just geting the props I care about in my logger service at exception time instead, and this worked well. It's better because you won't have code needlessly executing every time a property you want to log changes:

// app/services/logr.js
// initially generated with ember-cli-sentry's `ember g logger logr`
import RavenLogger from 'ember-cli-deploy-sentry/services/raven';
import Ember from 'ember';

const { Logger, inject: { service } } = Ember;

export default RavenLogger.extend({

  unhandledPromiseErrorMessage: '',
  user: service(),
  i18n: service(),

  addContext() {
    if (this == null) {
      // eslint-disable-next-line
      console.warn('logr cannot addContext because this is null/undefined, continuing without');
      return;
    }
    let tagsContext = {
      locale: this.get('i18n.locale'),
      id: this.get('user.id'),
      firstName: this.get('user.firstName'),
      lastName: this.get('user.lastName'),
      email: this.get('user.email')
    };
    // console.log('tagsContext', tagsContext);
    // For some reason setUserContext was not working, but setTagsContext was,
    // so I am using tags for all the user info. Maybe upgrading raven could fix this?
    this.callRaven('setTagsContext', tagsContext);
    // why use callRaven: https://github.com/damiencaselli/ember-cli-sentry/issues/58
  },

  // work around for unmerged PR:
  // https://github.com/damiencaselli/ember-cli-sentry/pull/97
  captureException(/* error */) {
    if (this.get('isRavenUsable')) {
      this.addContext();
      window.Raven.captureException(...arguments);
    } else {
      Logger.debug(...arguments);
    }
    return true;
  },

  captureMessage(/* message */) {
    if (this.get('isRavenUsable')) {
      this.addContext();
      window.Raven.captureMessage(...arguments);
    } else {
      Logger.debug(...arguments);
    }
    return true;
  }
});

For some reason the observer wouldn't work in my logr service..

Extra notes:

• with the ember-cli-deploy-sentry addon, don't forget to put THAT config in config/DEPLOY.js, not config/environment.js

To trigger an error somewhere in some application route hook:

setTimeout(() => {
  // I was having some issue with `throw new Error()` so I did this instead
  // It's actually just a better way to manually 'throw an exception'
  // because it will not forcibly crash the application, but instead
  // at least attempt to continue running
  this.get('logr').captureException(new Error('sentry user context test'));
}, 10000);

• Don't forget to set development: false to let raven actually send this test error to sentry (unless you aren't testing end to end) (I typically have this set: development: environment === 'development'

In application route actions, add this to your error action handler:

error(error) {
  // Trap unhandled failures during routing:
  // Should maybe be handled by the sentry addon, but is not as of now:
  // https://github.com/damiencaselli/ember-cli-sentry/issues/105
  this.get('logr').captureException(error);