Again, you can have arbitrarily large variances, nothing is stopping you from formulating a measurement process so horrible as to satisfy this. But that does not mean you can make arbitrarily small variances. The variances are physically related to each other. You need to find out what this relationship is and then you can find what are the limits that you are able to impose. You have been saying that you can get some variance that is such and such size that makes the required variance in the other observable unphysical. But you have not verified that you could make the first observable's variance arbitrarily small. You need to go through the physics of the experiment and see how the variances can be introduced and how they are related. Heisenberg's uncertainty principle already did this for some black box system. You want to see how it is enforced in your actual example system then you will need to work out the physics of the variances.
