Hello
The 4mm patch antenna give you a STRONGER, faster lock to satellites , I did not see extra satellites, only faster and stronger signal.
When I got my first phantom ( p2v ) it would take up to 5 minutes to hook to 6 satellites, then it would rock back and forth from 5 to 6 to 5 to 6, etc changing from GPS mode to ATTI, and back, I HATED IT! ( most I ever saw was 7 ) When I did 4mm upgrade, it locked within seconds to 6-7, back and forth, and would aquire satellites indoors.
Then later added GPS BOOSTER, and BAM went to 11, most I've seen was 13, but not too often, 11 mostly.
Now I've never had a problem! Always squire gps lock and home lock, even in my bedroom! It is crazy! But works!
As for distance,
I gave up when Ittelite antennas came out, p2v and up! Not sure if they make a p2 version?
But
I used cloverleaf first with not much luck, then went circular polarized ( left I think? ) but not 100% left or right ( LHCP OR RHCP )
They were pretty good
Then Diapoles came out they were even better, and you did not have to alter the craft, only Tx.
Then ittelite came in
Single unit for 5.8 Ghz tx and 2.4ghz wifi all on Tx , nothing on bird, went over 4 miles!
You are opposite
2.4 tx, 5.8 wireless.
I'm sure if you search here for antenna options for p2 ( under p2 mods ) might be more help!
I run ittelite on mine ( I fly the most ), others are stock! But t don't need any distance, for hobby and work! ( I build swimming pools, and keep a portfolio or pics and video ( ground and sky )!
( now I think about it, I think they do make a 2.4 ittelite version ) that would be the best bet, or wire the 5.8 one backwards ( does require Tx mod to accomodate the cable style ( smh ) I believe to mini fla connector ( if I remember correctly? Been a while ) lol
J Dot