how to compute channel capacity
Your proposal will not give you the channel capacity as defined in the Shannon-Hartley channel capacity formula.

The reason is that what the Shannon-Hartley formula tells us is that given a channel with a fixed SNR, there exists some coding scheme that achieves error-free transmission at the channel capacity. Put another way, the formula tells us the error free transmission rate we can achieve if we choose the best of all possible coding schemes. 

Since your proposal tests the error rate with only one particular coding scheme, it is not likely to achieve the optimum transmission rate. 

Actually finding the best possible scheme in all situations is not a solved problem and has been a major focus of communications research since 1948. That means we don't yet even know what all the possible coding schemes are, so there's no practical way to actually do a Monte-Carlo or other simulation to estimate the channel capacity.

In any case, why should we avoid using the formula? It's quite simple to calculate

$$C = B\log_2(1+\mathrm{SNR})$$