At Lanark Mart implement sales there are a lot of buyers from Northern Ireland (sorry I don't know if Cavan is in north or south). The most amazing loads get towed away from there heading for the ferry. The one that had us in stitches was an ordinary car towing a full-sized dung spreader. I doubt they had much steering as loads of weight was on the tow bar of the front wheel drive car, and there's no way the brakes could have stopped that lot. We wondered if they ever got there
There are frequently trailer loads of mixed stuff, piled high, and there seems to be no difficulty with getting them on the ferry.
You should get your stuff easily on a trailer if you have one, but there will be plenty of drivers doing the journey frequently who might be able to fit you in as a part load. I would suggest you identify the companies who do the route regularly and approach them.
Are you moving there? We have had extraordinary stuff taken in the removals lorry along with our furniture - motor bikes included, paving slabs, rotavator....