Using workers' income figures in specific sectors may be difficult, since some sectors relied a lot on slaves (e.g. mining), and others may have used different sources of manpower in different geographic regions (e.g. agriculture: free workers in Italy, slaves in Sicily). So the income aproach may be difficult.
Likewise, the expenditure approach may be complex, unless we have access to data on the consumption of goods (through the amount of taxation levied upon goods, perhaps?)
This would leave us with the production approach, i.e. determine the amount of goods produced in each geographical region, find market prices for these goods, multiply getting the production value per sector and per region.
Just an impression I have: maybe the Roman Empire is actually a good place to try this out, since a relatively small types of goods seem to have occupied a disproportionately large proportion of trade. Transport of olive oil, wine, wheat, metals (and slaves?) would cover a large part of what has been found in shipwrecks. Of course, this should not let us forget smaller production of goods not offered up for trade. Brassica in Campania would have mostly been consumed locally. But it may give a rough idea of the relative importance of productive sectors.
What I am wondering about is how to estimate the importance of the terciary sector. May not be easy when doctors, scribes, et al. will often have been slaves bought for the task.