Here is the build I use for Tour the Galaxy, including everything I could find to increase Sector Speed. My current personal best is 7 minutes 16 seconds for completing the full Tour the Galaxy:
UPDATE: As of 11/2021, a new sector speed trait is available: Synthetic Good Fortune, from the Equinox Pilot Scout Ship. The above run did not utilize this trait.
Credit where it is due, this guy reached the fastest known (at the time) speed using the Palatine Multi-Mission Reconnaissance Explorer with it’s special engine set: https://www.reddit.com/r/sto/comments/f9nt5s/new_sector_speed_record_achieved_warp_speed_14809/
This is my version, utilizing a Miracle Worker ship. This might be even better for doing Tour the Galaxy, because the Miracle Worker engines can have so much uptime.
Top Speed: Transwarp 132.55
120 second slipstream uptime, 10 second cooldown
Engine: Omega Force Hyper-Impulse Engines Mk XV [SecSpd-2] [Spd] *See note below.
Warp Core: Gamma Synergistic Overcharged Warp Core Mk XV This only needs upgrading to very rare.
Trait: Extensively Modified Warp Core This trait came from the Legendary Anniversary bundle and improves speed dramatically, but it is not required to complete Tour of Duty.
Buff: Diplomatic Immunity buff and the KDF counterpart, Raid Party.
Buff: Engineering doff assignment crit success buff (Perform Antimatter Containment Leak Drills).
Skill Tree: Sector Space Travel Speed
*Another engine option is the Adapted M.A.C.O. Combat Impulse Engines. These engines are a tiny bit faster in sector space, but they do not have the slipstream recharge that the Omega engines have. Recharge feels a little more nimble to me, but I think either engine is fine.
For completeness, here’s how (little) the Adapted MACOs speed advantage is:
|Sector||Slipstream||Slipstream w/ Traits|
http://logicker.net/tour/tour.html This guy’s discussion is an amazing read. After digesting it, these are the two maps I use.
I start at Nimbus (using the “Fist Full of Gorn” mission to transwarp to Nimbus), and then use the regular Transwarp to warp to Defera after completing Beta quadrant:
The speed scale differs between quadrant. Alpha quadrant gives slightly higher speeds than Beta quadrant.
Since sector space is still basically Champions Online in space, gravity is still (inappropriately) a thing: if you fly down you go slightly faster than if you fly up or level.
There appears to be a solar wind, or current! I found that I could go 0.01 warp factor faster if I was traveling downward from NW to SE, than I could if I was traveling from SE to NW.