~고서라도 == -고서 + 라도 == -고 + 서 + 라도. Detailed explanation of this phrase can get complicated, but since your Korean comprehension level seems pretty high, I'll go through it and give you a taste of advanced verb endings. -고서라도 involves three connective components. It might look unusual but it's actually a fairly common form. * -고: expresses two actions in sequence (숙제하고 자다), or two concurrent states (검고 푸르다). * -서: coming after -고, -(아/어), -에, etc. sharpens the first verb's meaning. For example, -고서 is a stronger "(something happens) and then ..." than -고. * -라도: after a verb, adds the sense of "even if it means (doing something undesirable)", "even if it is by doing ...", "even if it necessitates ... ", etc. There is also -더라도 which is similar but attaches directly to the verb stem. Given the variations in each of the three components, there can be several different expressions of this kind: -더라도, -고서라도, -(아/어)서라도, etc. Here are examples using 빚지다(take a loan), which conjugates to 빚지어 (빚져), and 빚지고. Their meanings are given in English while trying to differentiate them as much as possible. For practical translation, we can just use "even if it meant ..." for most cases. 1. 빚져(서) 집을 사겠다 (I will buy a house by taking a loan): -(아/어) + optional 서. 2. 빚지고(서) ... (... after taking a loan): -고 + optional 서. 3. 빚지며 (taking a loan): -며. (-며서 doesn't exist) 4. 빚지면서 (same as #3): -면서 (-면서 and -며 are about the same) 5. 빚져(서)라도 (even if it is by taking a loan): -(아/어) + (서) + 라도. 6. 빚지고(서)라도 (even if it is after taking a loan): -고 + (서) + 라도. 7. 빚지며라도 (even if it means taking a loan): -며 + 라도. 8. 빚지면서라도 (same as #7): -면서 + 라도. 9. 빚지더라도 (even if I take a loan): -더라도 directly after the verb. 10. 빚져야(만) 하더라도 (even if I have no choice but to take a loan): -져야(만) 하더라도 (even if I have to ...) 11. 빚진다(고) 하더라도 (even if it meant I'd have to take a loan): similar to -져야 하더라도, with a subjunctive feel. Most of these expressions are natural and are actually used. (continued)

고서라도 is a combination of 고서 and 라도 V-고서 " V and then " (same as V- 고 나서, V-고 난 후) Add verb stem to 고서 or 고 나서 or 고 난 후 숙제하고 나서 친구하고 놀았어. (Casual) -> I did my homework and then played with a friend. -(이) 라도 is a grammatical structure that expresses “even,” “even just” or “at least.” 심심하면 공부라도 해! If you are bored, at least do some studying. V-고서라도 means "even if V" 다음날의 피로를 감수하고서라도 새벽 중계를 챙겨본다. I never skip to watch the broadcast at dawn even if I take a risk of exhaustion of the next day. 잠이 안오니 수면제를 먹고서라도 잠을 자야겠어요. I should sleep even if I take sleeping pills because I can't fell asleep. 택시를 타고서라도 빨리 다녀오겠습니다. I will come back quick even if I take a taxi.

With that in mind, your example sentences may be translated as follows. 다음날의 피로를 감수하고서라도 새벽 중계를 챙겨 볼 만큼 올림픽이라는 대회가 의미 있는 지구촌의 행사임을 알 수 있다 (감소 -> 감수). => We can see the Olympics is an event significant enough for us to not miss the wee hour broadcasts even if it means enduring a groggy day because of that. 잠이 안 오니 수면제를 먹고서라도 잠을 자야 겠어요. => Nothing seems to help, so I'll have to get some sleep (even if it is) by taking sleeping pills. 택시를 타고서라도 빨리 다녀 오겠습니다. => I'll make it back quickly even if it meant taking a taxi.