This question is really interesting. I never thought about it that way.

First of all, I'd like to suggest 〜ところで as the equivalent conjunctive particle:

• いきなり言われたところでわからない (= いきなり言われても〜)
• 急に来られたところで会えない (= 急に来られても〜)
• ぜんぶ頼まれたところでできない (= ぜんぶ頼まれても〜)

I tried to reverse engineer a catch-all translation that is better than even or although, and I think it's but:

• いきなり言われても〜 Tell me out of the blue, but I wouldn't know.
• 急に来られても〜 Come unannounced, but I wouldn't be able to see you.
• ぜんぶ頼まれても〜 Ask me to do everything, but I wouldn't be able to.

Try it out with more examples here and here.

Side Note: To stretch it a bit, you can maybe even rephrase the other sentences to fit this conceptual mould, too:

• 食べてもいいよ → 食べたところでかまわないよ

Eat it, but I wouldn't mind.

• 先生でもたまに勉強する → 先生であったところで勉強はする

Being a teacher, but still study.

• 高くても買う → 高かったところで買いはする

Be expensive, but I'll still buy.

This question is really interesting. I never thought about it that way.

First of all, I'd like to suggest 〜ところで as the equivalent conjunctive particle:

• いきなり言われたところでわからない (= いきなり言われても〜)
• 急に来られたところで会えない (= 急に来られても〜)
• ぜんぶ頼まれたところでできない (= ぜんぶ頼まれても〜)

I tried to reverse engineer a catch-all translation that is better than even or although, and I think it's but:

• いきなり言われても〜 Tell me out of the blue, but I wouldn't know.
• 急に来られても〜 Come unannounced, but I wouldn't be able to see you.
• ぜんぶ頼まれても〜 Ask me to do everything, but I wouldn't be able to.

Try it out with more examples here and here.

Side Note: To stretch it a bit, you can maybe even rephrase the other sentences to fit this conceptual mould, too:

• 食べてもいいよ → 食べたところでかまわないよ

  Eat it, but I wouldn't mind.

• 先生でもたまに勉強する → 先生であったところで勉強はする

  Being a teacher, but still study.

• 高くても買う → 高かったところで買いはする

  Be expensive, but I'll still buy.