What ship is then best for "faction rank grind" and is there a way to accelerate this grind to (hopefully) half a week or (unrealistically) a day? 7 days with 4-5 hours of grind does not sound optimistic at all
The grind to the rank is real, that's why I'm not doing it. I will eventually get into the bigger ships, there are other things to do while working towards that goal. I wouldn't say that there is a ship that is better, you will be doing a multitude of missions. I like to go to places that will offer Charity Missions, spend some Credits and rank up that way. My goal when I do the Rep grind is to never have to leave the station. I will load my Anaconda up with Fruits and Grain, Fish, and other common items (I can't remember them or I would put them here!), then park it at the station accept missions, give money or goods, and repeat. When I get bored, I go pick up some rare goods, head back to the starting system (LHS 3447) to help and advise new players, then it's off to go combat piracy at my favorite HAZRES. I try not to only focus on the hunt for the biggest ship, I will get burnt out way too fast!
Sylar, the buff to the FDL is in the patch notes and also has been talked about on numerous Podcasts and videos. Take a look here at the 1.5.3 patch notes.
https://forums.frontier.co.uk/showthread.php?t=201170
Zac mentions the increase in Maneuverability, heat dissipation, and increase in power.