Cutting 14mins off Portsmouth direct trains is probably acheivied by combination off removing stops and reducing dwells quite a few are very generous. In the down direction there is pathing time approaching Havant, 2 minute dwell at fratton and Portsmouth harbour which is also matched with very robust running times fratton to Portsmouth Harbour.
Additional Portsmouth to Southampton service is excellent idea hopefully it will run 30mins apart from the FGW portsmouth Cardiff services. Part of the reason the current service is so unpopular is that they you can leave Southampton 20mins later and arrive at almost the same time.
Making the Portsmouth to Southampton effectively be the stopped to Brockenhurst and Weymouth will make many cross Southampton journeys palleteable compared with really bad journey times at the moment.
I think it will be an interesting to see the proposed timetable and particular interesting to see what the consultation includes in detail.
Cutting 14 mins off on the down would be tricky. If you get a clear run with a 1Pxx service you can do Woking in ~20' & Guildford in 28', but that's "driving it like you stole it". So Woking in 21' & Guildford in 30' is perfectly achievable.
Again with a clear run:
Guildford - Haslemere = 13'
Haslemere - Petersfield = 10'
Petersfield - Havant = 12-13'
Havant - Fratton = 8'
Fratton - Southsea = 4
Southsea - Harbour = 5'
With station call allowances more or less as they are, that would give you an approximate journey time of 92' for a 77 mile journey.
If you deleted Woking & Haslemere from the equation (which you're not allowed to do) but for arguments sake we will, that would bring it down to ~85' which is somewhere where it used to be.
However you have the gruesome twosome which are always late & are for always getting in the way and that's SN & GW at Havant & Guildford respectively, so a ball park figure of 90' should be achievable in theory.
That's just 7' quicker than what it's done today, taking the amount of time out you're suggesting without removing Woking, Haslemere, Petersfield and Havant out of the stopping pattern, just isn't going to happen.