Okay, so I tried beelining on the same setup as previous two games. I was able to draw Star Fortresses tech card in the end of 2246 which was 9 years earlier than on my focused run. So, it is definitely working and I have observed some interesting behaviours, which, I believe, will allow to speed up process even further.
My assumptions were:
1) Star Fortress' card may be forced into pool way before 2250 if there are no suitable tech cards (due to not met special conditions / missing prerequisites / not enough lower tier techs researched) -
correct
2) all technologies with higher weights (probability) than Star Fortress must be researched first -
not correct
3) higher tier techs are unlocked based on number of researched techs across all three fields -
not correct
4) it is possible to block tech card by reverse-engineering debris -
correct
Based on these I decided to ignore techs which unlock the most of other techs: Coilguns and Destroyers from Engineering, Colony Centralization from Society and Fusion Reactors from Physics. As I wanted as many tech alternatives as possible, I as well skipped Blue Lasers to draw Self-Evolving Logic as fast as possible.
+++ WALL OF TEXT +++
So, let's take a look at the research history:
Tech Card 1 (tier) / ... /
Tech Card to research (tier) / ... / Tech Card N (tier) / (Reverse Engineered Tech Card 1) / ... / (Reverse Engineered Tech Card N) - Researched Tier 1 Techs / Researched Tier 2 Techs
Fusion Reactors (1) / Quantum Theory (1) /
Global Energy Management (1) - 0 / 0
Planetary Unification (1) / Space Trading (1) / Biodevirsity Studies (1) - 0 / 0
Powered Exoskeletons (1) / Geothermal Fracking (1) / Nanomechanics (1) - 0 / 0
Improved Corvette Hulls (1) / Ceramo-Metal Materials (1) /
Robotic Workers (1) - 1 / 0
Improved Deflectors (1) /
Automated Exploration Protocols (1) / Blue Lasers (1) - 1 / 0
Adaptive Bureaucracy (1) / Global Defense Planning (1) /
Neural Implants (1) - 1 / 0
Nanomechanics (1) /
Geothermal Fracking (1) / Coilguns (1) - 2 / 0
Databank Uplinks (1) / Quantum Theory (1) / Fusion Power (1) - 2 / 0
Field Manipulation (1) / Blue Lasers (1) /
Administrative AI (1) - 3 / 0
Mineral Processing (1) / Afterburners (1) / Ceramo-Metal Materials (1) - 3 / 0
Biodevirsity Studies (1) /
Eco Simulation (1) / Space Trading (1) - 2 / 0
At this step I had researched a total of 8 tier 1 technologies, but none from tier 2 have appeared. That's how assumption (3) was proven incorrect. As such, I will list only Engineering techs further:
Nanomechanics (1) / Carrier Operations (1) / Standardized Corvette Patterns (1) - 4 / 0
Afterburners (1) / Machine Template System (1) /
Improved Corvette Hulls (1) / Ceramo-Metal Materials (1) - 5 / 0
Destroyers (2) / Ion Thrusters (1) / Standardized Corvette Patterns (1) /
Starhold (2) - 6 / 0
As soon as 6 technologies in Engineering were researched I got tier 2 techs as options. At this point I have unlocked +1 research alternative.
Machine Template System (1) /
Modular Engineering (2) / Afterburners (1) / Ceramo-Metal Materials (1) / (Ion Thrusters) - 6 / 1
I've got Ion Thrusters from mining drones. From this point on, it will not appear among "normal" tech cards - assumption 4 was correct.
Destroyers (2) / Orilium Mining (2) / Advanced Corvette Hulls (2) /
Assembly Patterns (1) / (Ion Thrusters) - 6 / 2
Afterburners (1) /
Standardized Corvette Patterns (1) / Coilguns (1) / Machine Template System (1) / (Ion Thrusters) - 7 / 2
Another +1 alternative from now on. Note the interesting pattern - as I have so many alternatives, techs from odd lines will not appear in the even lines. This is due to tech's weight being halved after appearing as an option.
Orillium Mining (2) / Destroyers (2) / Space Torpedoes (2) / Carrier Operations (1) /
Improved Structural Integrity (2) / (Ion Thrusters) - 8 / 2
Machine Template System (1) /
Advanced Corvette Hulls (2) / Ceramo-Metal Materials (1) / Coilguns (1) / Afterburners (1) / (Ion Thrusters) - 8 / 3
Destroyers (2) /
Space Torpedoes (2) / Carrier Operations (1) / Orillium Mining (2) / (Ion Thrusters) - 8 / 4
Coilguns (1) / Afterburners (1) / Ceramo-Metal Materials (1) /
Machine Template System (1) / (Ion Thrusters) - 8 / 5
Something strange is happening - I should have 5 research alternatives, but game gives only 4 techs! It seems that if the tech was in the previous draw it will not appear on the next one at all! This proves assumption 2 wrong and changes the whole approach of which techs should be blocked to force desired card to be drawn.
Destroyers (2) / Carrier Operations (1) /
Orillium Mining (2) / (Ion Thrusters) - 9 / 5
Ceramo-Metal Materials (1) /
Afterburners (1) / Coilguns (1) / Armored Torpedoes (3) / Construction Templates (3) / (Ion Thrusters) - 9 / 6
It went down to mere 3 techs on odd draw. Again, as soon as 6 tier 2 techs were researched, tier 3 started to appear.
Destroyers (2) / Carrier Operations (1) /
Star Fortress (3) / (Ion Thrusters) - 10 / 6
Finally, Star Fortress appeared, with no other tier 3 options present. Assumption 1 is correct.
+++ WALL OF TEXT ENDS +++
So, I've got desired tech on second draw after unlocking tier 3. Now, due to odd/even draws behaviour, one can block not mere 4 but a whooping 8 techs - I think it could be easily done 3-5 years earlier (I researched some expensive rare techs and had 4 tier 1 techs more than needed).
I'll post comparison between run #2 (focused) and run #3 (beeline) a bit later.