You can join pieces of felt but I'm not sure how the "seams" would look. Is this for one of your large felt pictures? If so, I guess the challenge would be covering the seams or incorporating them into the design.
Perhaps it could be a variety sizes of squares and rectangles in the same theme that would be connected, emphasizing the seams instead of trying to make them disappear. Kind of like a pieced quilt.
When joining pieces of felt, leave the edges softer and then put wool roving in between the pieces that are being seamed together. The roving will be like glue to hold the seams together. Remember that the wool from behind and the glue wool will probably end up showing on the front so you'll need to work out the colors and the look of the seams with sampling.
With regard to fitting it under your sewing machine, I wonder if this would be of interest to you? The method for large pieces is that you only have to work on one quarter of your piece at a time, and that wouldn't be any larger than the pieces you've already done on your machine.
As for the actual felting, are you able to erect a temporary 'building' (perhaps a cheapo pop-up gazebo with zip-in sides) in your garden and beg/borrow some fold-up picnic tables that you could put together to make a large working area?
Just remembered - Zara posted a little while ago a large project she made on a trampoline.