#1
I need new strings for playing in C#/C on an Epiphone Thunderbird. At present I use a DR Strings DDT-55 set (55/75/95/115) and they’re too taut and stiff; playing Children of the Grave with these strings actually makes my hands and forearms hurt. For comparison, I can tune the D’Addario 45–130 set on my five-string up to C and there’s less tension than the DDT-55 set has in C. I need strings that will have tension comparable to the aforementioned D’Addario set in C# and be a little loose in C. This bass gets used mostly for Sabbath along with some doom and stoner rock (Monster Magnet, Kyuss, Sleep), so I don’t need a punchy modern metal sound.
#3
I know this seems strange, but before you go buying new strings, try to play with your setup a bit. I had a love/hate relationship with my drop C# jazz until I tightened the truss rod a bit and lowered the action. Plays like a dream now!

If that doesn't work though, can't go wrong with Ernie Ball. After what you said I'd try out Power Slinky strings. Bit thinner than what you're currently rocking