I've not been stuck. Considering people have taken the time and effort to provide a list of quests a week before the event starts on live servers you could have opened up several provinces before hand and left them alone until the quest for relics came up. I opened up 2 which I used for Q17. On Q37 I did another province which finished scouting
20 mins (<timed it almost perfectly! before I got to the quest, that was another 8. I had 1 from NH and then 12 from a large egg. Job done.
You will have plenty of time to scout province for the last quest requiring relics. Q77 for 32 relics. That's 4 provinces to scout in the next 27 days ;/. However you will have tournament relics from tomorrow and even if they are not your boosted goods, either do them or don't bother and wait till the next tournament in your boosted goods. There is still 27 days to go (3 tournaments).
You will probably become stuck for a few days waiting between Q57 > Q66 because 5 spells are needed. So thats 65hrs. Even though I'm almost at 57 now. Tomorrow evening I'll be at Q66 waiting for 3 spells. While I wait 2 provinces open ready for 16 relics Q77 + 15 from 8 lvl 1 tournament provinces + 1 from NH.
Provinces in tournaments now are very easy to auto-fight so 8 is achievable and cheap resources wise anyways.