I use Niemeyer instead of puppet. This is slightly different.
I didn't really discuss these with my partner (except the 2NT-3NT that we always forget

), but could try to handle it with:
=> Minors:
With slammish hands I porbably bid:
transfer with 3S and bid minor on 4 level. (forcing), this asks for control bids.
OR
3C niemeyer followed by 4C minor suit stayman if you want to know the distribution.
With non-slammish hands similar if I my hand cries for 5m, but probably go to 3NT (via 3C)
=> with majors:
--- Non slamish:
------- bid 3NT with 5S/4H
------- transfer to H (3D) and bid 3S with 4S/5H
------- transfer to S (3H) and bid 4H with 5S/5H
--- slamish:
------- No problem with 4S/5H because the 3S bid is still forcing
------- Problem with other hands, 3C niemeyer followed by 4C minor suit stayman could be a possibility to get the distribution and put the contract afterwards.
- 5 spades/4 hearts hands (e.g. Smolen-type; how do you bid them if using 3S as Minor Suit Stayman)
=> 2NT-3NT: 5 spades and 4 Hearts. (We go through 3C to end in 3NT). This is an agreement we easily forget!!!
- if the scheme you are suggesting means giving up 4C Gerber in place of another meaning, how do you ask for aces.
=> Only 2NT-4C is Gerber. Otherwise ask aces with 4NT