The retooling cost in VB6 was 0.5x build cost plus 0.25x build cost per slipway. I cannot find a more recent source for C#, but from observation and testing I believe that the "build cost" is actually the
cost to refit from the current class to the new class. This means that if you want to retool a 20x1000 ton shipyard to a fighter class with, say, 90 BP refit cost from the old class (cost of Steve's Viper Mk III plus a 20% premium - assessing the "worst-case" of almost no overlap between two very different classes), your total retooling cost is 90*(0.5+0.25*20) = 495 BP. Assuming a total BP per annum of 12,000 as in the OP, that's about a fifteen-day refit period, maybe 20 depending on your construction increment. 2-3 weeks out of the year isn't a terrible cost, although it is still advisable to keep a healthy reserve of planetary factories for on-demand build orders.
This does depend somewhat on your fighter doctrine, if you use 250-ton fighters the build costs and thus refit, etc. are about half as much as if you use 500-ton fighters, for example. Plus doctrinal differences about engine power modifiers, weapon types, and so on can make a big difference.
But basically it seems the evidence in thread suggests that a mix of fighter-scale shipyards and planetary factories is the ideal approach, the shipyards for efficient mass production and the factories for flexibility and building limited-run craft such as specialized scout craft. Maybe 2-4 shipyards instead of one monolithic complex is ideal if you use a few different main classes - missile bomber, railgun interceptor, small scouts, and so on.
Another consideration I haven't seen mentioned is broader economics, as at some point there is no point in a bigger shipyard (or more factories) if you can't afford to keep building fighters, for example a gallicite crisis is a common enough problem. However I'm not sure how that really impacts the discussion here if at all.