Its not a case of the fastest yeast, its more a case of how quiclky you can get the beer to be drinkable. Under favourable conditions yeast will finish fully fermenting out when its ready, not before. Rushed fermentation will lead to all sorts of problems, just let it do its thang.
Ive consulted by boss (ex pro brewer) on this matter before, he is also a advocate of young fresh beer.
Ferment for 2 weeks, rack into a secondary with gelatine leaves...leave for 1 week. Transfer to a bottom tapped keg with more gelatine. This will drop clear in 3 days and is ready to drink. This suits "milds and old ales" perfectly...of course it wont be carbonated, but IMHO they shouldnt be. Ready to drink within 1 month.
P.S. Dont but gelatine leaves, PM me and Ill send you some for free.
HTH
The only downside is that it must be drunk within 3 days