Cross-processing can produce some interesting results. A Web search should turn up plenty of examples. Whether it's a "good idea" to try cross-processing with your expired film is a subjective question. If you're going for a surreal sort of feel and/or odd color shifts, then cross-processing may get you exactly what you want. I wouldn't recommend it for situations where accurate color reproduction is important. (Cross-processed wedding photos? Most couples would kill you if you were the hired wedding photographer.)
Since you say you've shot several rolls of this film, you might want to consider cross-processing one or two of them to see what you get, and decide whether to cross-process or normally process the remaining rolls once you see the results. Keep in mind that different brands and types of film can respond very differently to cross-processing. I've only cross-processed three rolls of E-6 film so far. Two rolls of Kodak Elite Chrome 200 produced almost normal color (when scanned; I haven't done any conventional prints from them), but a roll of Fuji Astia 100 produced results that were so off they were almost useless -- the negatives were dominated by light cyan, making it difficult to get a good range of colors. (OTOH, this roll was also cross-processed night shots, which may have something to do with the color response.)
One more point: You refer to a commercial minilab. Some minilabs refuse to cross-process film. Others will do so, either out of ignorance/sloppiness or because they understand the process and are willing to do it.