It sounds to me like you are embroidering pieces that you sew together to make a quilt, as opposed to having a whole cloth top on which you embroider. If that's the case, then you could use a multitude of QAYG or quilt in sections techniques on a domestic sewing machine.
As others have indicated, there are LAQs out there that would be happy to quilt your large embroidered quilts. You need to ask yourself ...
How many of these large, king size, quilts do you plan on making?
How much would it cost to have that many quilts done by someone else (get several quotes)? Is that less than the cost of a LA machine with maintenance, etc?
Do you have a large amount of space to dedicate to a LA machine?
Do you want to spend your time doing LAQing or machine embroidering?
As someone else mentioned, do you want to turn your hobby into a business?