Some gearbox questions for my 6N2 GTI

Hello everyone. It's been a while since last time I came here looking for solutions for my 2000 6N2 GTI gearbox. 
Basically, at the moment I have my Polo at the mechanic for an engine rebuild, I also decided to take apart the gearbox that I'm currently running at, a 085 DKG gearbox from a 1.0 6n  as I made a little crack in the housing near to the mount days before the rebuild. The gearbox is very short ratio, it is fun in the mountains but quite annoying on motorways. So I thought about changing the final drive of the actual box to a diff/ pinion from a 1.4 engine, so it can get a little bit longer but not as long as the GTI that comes from factory. Until here it's been clear for me, the solution is simple, as I only need to get another final drive and put it on the one I have currently. Once my Polo is already being all opened up, I thought about getting rid of that sloppy shifter. I had in mind to get a OEM shifter from a mk4 golf, Bora, a3, ibiza and so on, but I'm not sure if it would be a direct fit to the 085 box I have on my Polo. My girlfriend has a Lupo GTI and the shifter feels precise and solid and I'd like to have the same feeling on mine. The questions are... Could I get a 02T housing and fit all the gears from my 085 in it?  to get a shifter from these series ? Are 02T boxes a direct fit to my car? If not, can I just get a shifter and fit it directly on my085 box?

Any suggestions and ideas are welcome, I've been doing my research for weeks about gear ratios, combining available parts and compatibility with what I have and what I want to get, so I'm getting confused at this point  😅

Kind regards from overseas, Lisbon Portugal  :)