But your argument requires exactness. You can't talk about a fine tuned universe if you do not know the exact values of the constants for that fine tuning.
You don't need to be able to measure exact value to know a value is constant. IF a plastic cup can only hold 16 oz. of water, it makes no difference whether we are able to measure ounces accurately, the amount the cup will hold doesn't change.
Let's take our analogy to a higher level to represent the universe and uncertainty principle. We have a pool in the back yard... the value of water in ounces that pool can hold is constant. We understand this from the start, the pool can't gain or lose capacity. When it comes down to defining an actual set number of ounces the pool can hold, it is difficult to measure because of other variables which are not constant, floating around while we're trying to measure a result. Air pressure on the surface of the water is fluctuating in different parts of the pool, we see the water on the surface making ripples and waves... Some of the water we've measured has evaporated since we began the measuring, the temperature fluctuates and water molecules expand and contract, sediments in the air and impurities are constantly displacing molecules of water in the pool.... SO we can't ever know the exact precise number of ounces the pool will hold, but that constant value exists and we know that it does in spite of variable uncertainty. We even have a formula to determine a fairly accurate constant value. A standard 25m x 50m Olympic pool holds 660,000 US gal. Times 128 ounces per gallon, equals 84,480,000 ounces. Our formula results in an approximate value. We cannot measure the value any more accurately because of other floating variables happening as we try to measure. This does not change the true precise capacity of the pool.
Now, to put the final touch on this analogy, imagine if our pool could not have the capacity of one drop of water, more or less, or it can't physically exist?