@JasonPatrie,

You can use JavaScript to split the string into 1000 character chunks and set embedded data fields for each chunk. I would do it in the addOnPageSubmit function of the text entry question. You will need to define embedded data fields for the maximum number of chunks in the survey flow prior to the block containing the text question.

 @JasonPatrie The question where you are collecting the text input from add the below JS 

Qualtrics.SurveyEngine.addOnload(function() {
    var that = this;
    function splitTextIntoChunks(text, chunkSize) {
        var chunks =  ];
        for (var i = 0; i < text.length; i += chunkSize) {
            chunks.push(text.substring(i, i + chunkSize));
        }
        return chunks;
    }
        function setEmbeddedDataFields(text) {
        var chunks = splitTextIntoChunks(text, 1000);
        for (var i = 0; i < chunks.length; i++) {
            var embeddedDataFieldName = "ResponsePart" + (i + 1);
            Qualtrics.SurveyEngine.setEmbeddedData(embeddedDataFieldName, chunksni]);
			//console.log(embeddedDataFieldName + ": " + chunksni]);
        }
    }
	var qid = this.questionId;

    var textField = document.getElementById(qid).querySelector('.InputText');
    textField.addEventListener('input', function() {
		    var textResponse = textField.value;
        setEmbeddedDataFields(textResponse);
    });
});

Your embedded datas will be named as 
ResponsePart1

ResponsePart2

ResponsePart3 and so on these will be created automatically after every 1000 chars.

Hope it helps!