You'd discover items or encounter events that would unlock research topics each topic had a cost in the six different science fields. Once you paid that cost it would take a period of time before you received the results of the research.
I've always had an appeal for a system where there is a "cause for breakthroughs".
Such, a lot of empirical research can be ongoing on relatively mundane topics, but most of the breakthroughs origin from "odd discoveries" such as: we have a mutant, or stellar samples have been recovered, etc. Science gets boosted by discoveries as even the smallest thing can put a new perspective on everything we already have and we think of new tests to do on things we thought we knew etc.
So, finding traces of long gone civilizations should probably improve scientific progress by quite a margin.
Since your game is single player, and greatly asymmetrical, why not introduce such physical components on some of the planets? Finding ruins from older species and researching them might net you some advantage. Perhaps tying these unique researches to specific objects in the map so that some (many, if not all) techs can only be researched once their object has been found and researched. Would also prevent from having to deal with scientists constantly falling idle: instead, they're always assumed to be "working", but can research particular objects in hope that there's more to learn from them.
One implementation of such a system could be as follows:
Your team can only research one item at any given time. That item yields science pts (undisclosed amount). That amount reduces as technologies from this item are discovered, but science pts can still be used to progress towards more general technologies (improving engines, etc.)
"Broke Rune of Ku'lak"
Gives 100 science pts per turn investigated.
Unique tech 1 - 1000 pts: Morale +5% empire wide "The teachings of Ku'lak" (from here on, this artifact yield only 80 pts/turns)
Unique tech 2 - 3000 pts: Morale +10% empire wide "The covenant of Ku'lak" (from here on, this artifact yield only 60 pts/turns)
Unique tech 3 - 5000 pts: Morale + 15% empire wide, resist riots + 10% "Ku'lak's reign" (from here on, this artifact yield only 30 pts/turns)
Progress towards unlocking these techs is only accounted for while this item is selected.
Any points given by this artifact also translates to all other mundane techs being researched.
All mundane techs could be concurrent but have variable costs. Since progress towards each tech is measured by the same points, you can have some techs cost more or less depending on the order you want them unlocked, but some artifacts could mess up with that.
Engines I (1000 pts) Speed + 5%
Engines II (2000 pts) Speed + 10%
Warp-Drives (3000 pts) Fuel Cost - 10%
An artifact could have Warp-Drive as one of its "unique techs" meaning progress towards its realization might be twice as fast, meaning that having such an artifact in-hand would insure you can get Warp-Drives unlocked before Engines II
(focusing on techs would then become irrelevant)
Just a few random thoughts, of course.