I was just working on this yesterday. I found a way where I can store the values of a checkbox field in a free text field as a string of 0's and 1's to represent checked or unchecked, then save that value to the DB. On a lookup, another JS script will iterate through those values and either check or uncheck the checkbox appropriately. My script is a little long because it accounts for checkbox fields that are part of a collection, and a checkbox field that isn't, but here it is:

    //#region Convert from checkboxes to string for selection storage in DB

    // adds the event listeners to every appropriate checkbox on the form
    function addListenersToCheckboxes() {
        $('.documents-checkboxes .choice input').change(event, populateBinaryFields);
    }
    // runs the function one time on form load
    addListenersToCheckboxes();
    // When they add a new property, runs the function to add event listeners
    $('#q66 .cf-collection-append').click(addListenersToCheckboxes);
    // function that the listeners execute. Finds its correct string values input, and runs the script
    // to convert the selected checkboxes to a sequence of 1's and 0's
    function populateBinaryFields(event) {
        // targets the input for all collections
        let checkboxValuesField = $(event.target).closest('.rpx').find('.checkbox-values input');
        // if it's not an iterable, hard-code its checkbox-values input field
        if (checkboxValuesField.length === 0) {
            checkboxValuesField = $('#Field89')
        }
        
        // runs through each checkbox of the target checkbox's collection, determines if it's checked or not, and
        // creates a string
        let valuesArray = [];
        $(event.target).closest('.documents-checkboxes').find('.choice input').each(function () {
            if ($(this).is(':checked')) {
                valuesArray.push('1')
            }
            else {
                valuesArray.push('0')
            }
        });
        //populates the value of the checkbox values field with the string value determined above
        checkboxValuesField.val(valuesArray.join(''));
    }
    //#endregion

    //#region Converts from the string to checkbox selections for population on the form
    // Does the opposite of the above function. Takes the string value from the lookup and checks/unchecks
    // the checkboxes based on the string.
    function populateCheckboxes() {
        $('.checkbox-values input').each(function() {
            const valuesArray = $(this).val().split('');
            let checkboxField = $( this ).closest('.rpx').find('.documents-checkboxes');
            if (checkboxField.length === 0) {
                checkboxField = $('#q87');
            }
            valuesArray.forEach(function (value, index) {
                const checkbox = $( checkboxField.find('input').eq(index) )
                if (value === '1') {
                    checkbox.prop('checked', true);
                }
                else {
                    checkbox.prop('checked', false);
                }
            })
        })
    };
    populateCheckboxes();
    //#endregion