Just been looking at Siubhan's blog - the answer to your "can I take the rigid heddle weaving off the loom?" is "don't worry".
I have woven a couple of braids that were really too wide for my loom, so the unwoven warp kept falling off the shed sticks and mucking up the tension. So I just unwound a bit, evened it up and then rewound it. The braid I am currently weaving is not only too wide but has a cotton warp that has absolutely no forgiveness in it - I have had to unwind it several times and reattach it to the apron - and I can see that I will probably have to do it again.
So if when you take the braid off the loom the tension goes wonky, just even it out and reattach it to the apron - this is much easier if you have someone to help you by holding the other end. And as it looks like you are using a wool warp it will probably have enough forgiveness that you won't need to reattach it completely
By the way, the braid looks georgeous :-)
PS If any of this doesn't make sense - email me