This is not an area I've done a lot of work in, so keep that in mind when reading.
If your scenario has a set number of starting cities per Civ, that might explain such accelerated tech rate? But you mention map size, so I'm guessing everyone starts with 0 cities. Or perhaps you have special buildings that also increase research?
So you have the 'cost' field in the Civilisation Advance rules page with extremely rough tech cost averages of 40 for Ancient 80 for Medieval, 120 for Industrial and 250 for modern. So something along those lines might be appropriate?
Or more simply, if you are getting a tech every 4 or 5 turns per tech with 50% research then I'd suggest as a minimum you need to at least double the tech cost so that this becomes 4 or 5 turns per tech with 100% research in a government type with a trade bonus and not excessive corruption.
In terms of map size variations, this should be catered for with the default rules setting under the 'World Sizes' category, which has a 'tech rate' field. This figure should increase as map size increases except in certain circumstances (e.g. I intend the human and AI to have broadly the same size of empire on every map size from small to huge+ (206x206) as I keep the ratio of land tiles to number of Civs roughly the same across all map sizes and have settings to make mass conquest very difficult. So my tech rate is slightly increased from Small to Standard and then the same for Standard and above).
I think the first thing you have to do before anything else is establish if your teching issue is across multiple map sizes or just in relation to one map size. If it is the latter it is more likely to be an issue with the 'tech rate' field. If not, then it is probably a case of going into all your new techs and at least doubling their cost.
Hope the above helps.