Interesting............. if they are not running a wastgate, then they have either used:
1. oversize turbo (to prevent over spooling at full power at max revs)
or
2. an exhaust restrictor to do the same.
as an example, Mid 80's Mazda 323 1600 DOHC Turbos, utilised a 1" (25mm) restrictor plate in the rear muffler flange to prevent turbo over spooling, if you took it out you gained almost 50bhp without doing anything else! .......... but then you needed to fit an external wastegate to stop the turbo from crapping itself.
So to answer your question, swap out the old turbo with no waste gate, for the later model turbo with the wastegate and the lag should be much better.
then fit a 3" Exhaust and you should start to boost at 1000rpm
While a 3" exhaust is good for 300bhp on a non turbo engine, (~2.5" = 250bhp and 2" = ~120bhp) with a turbo you need 3" for anything over 150bhp to stop lag..... but still ok up to 1000bhp
I good mate of mine in the performance tuning game builds up street legal 2L Mitsi Evo engines to make 400-500bhp.
he was the race mechanic for the NZ GT1 class, on an old Evo2 with a 2.2L engine making 750bhp! ......... but the gearbox only lasted a weekend ......... was still the class winning car 3 years running up against 6L v8 Holden's, a TVR Tuscan, and a V10 Viper!