Ungrammatical text poses significant challenges for off-the-shelf dependency parsers. In this paper, we explore the effectiveness of using synthetic data to improve performance on essays written by learners of Swedish as a second language. Due to their relevance and ease of annotation, we restrict our initial experiments to word order errors. To do that, we build a corrupted version of the standard Swedish Universal Dependencies (UD) treebank Talbanken, mimicking the error patterns and frequency distributions observed in the Swedish Learner Language (SweLL) corpus. We then use the MaChAmp (Massive Choice, Ample tasks) toolkit to train an array of BERT-based dependency parsers, fine-tuning on different combinations of original and corrupted data. We evaluate the resulting models not only on their respective test sets but also, most importantly, on a smaller collection of sentence-correction pairs derived from SweLL. Results show small but significant performance improvements on the target domain, with minimal decline on normative data.