Your grass is a mix of different varieties. Although several are part of the Fescue family, each will taste different to your bunnies. So in my view there is nothing wrong with your grass mix. Are you intending the grass to provide a substantial part of your rabbits' diet, or do they also get lots of hay? Personally I think your rabbits will 'get used' to the new taste of the grass, which btw will vary throughout the growing period ie newly emerged grass will taste different to the same species when it is mature. Don't forget also that your set of grasses that you have currently will increase as other grasses move in, probably quite quickly.
We have a large square patch in the garden, which we leave to mature and seed every year. Have done this for around 20 years. All of it has arrived naturally ie we have not introduced any flower or grass seed, nor has it ever had pesticide or fertiliser. I developed an interest in grasses a few years ago, bought a field guide and attempted to identify all of the grasses in the hay patch, including their percentage. Looking at your Meadow mat, I reckon we have most if not all of the species mentioned. But, they are not in similar numbers. Certain species, probably the more vigorous, outnumber by far the rest. Our patch also contains a large variety of wildflowers, including I think most if not all of the ones listed in the Meadowmat. Again, it is very noticeable that some species will grow more vigorously and become 'bullies' to the rest.
I have looked at the description of the Meadowmat. I can't find any detail of the different percentage of both the grasses and the wildflowers, but possibly haven't been looking in the right place. There are also other wildflower species which I would not feed to my bunnies, including Black Medic and Selfheal, both of which are very vigorous here.
If this were my grass, I would leave it as it is and agree with the comments from Shimmer and Graciee. Not all of the species in the Meadowmat will be suited to your soil and where you live. That's why some of the more specialist wildflower seed companie will sell different mixes to take account of this. In my view it would be far better to develop a patch, which has been created with the seeds, currently in your soil, as they will grow more satisfactorily.