should/would after so-that clause

The sentence needs an auxiliary (would, could, might), but should is not a good fit.

WOULD IS BETTER

As a rule, clause of purpose, specifically so that clause, is followed by an auxiliary. To avoid sounding unnatural or prevent yourself from making a mistake, I recommend that you use can, will, may in the present, and could, would, might in the past.

"He wakes up early so that he can/will catch the 8 o'clock train."
"He woke up early so that he could/would

MaroldAs a rule, clause of purpose, specifically so that clause, is followed by an auxiliary. To avoid sounding unnatural or prevent yourself from making a mistake, I recommend that you use can, will, may in the present, and could, would, might in the past.

Thank you, Marold for the rule. Now, it's clear

Aspara Gus (...) should is not a good fit.

Thank you, Aspara Gus!

Ok, thanks

"He woke up early so that he should/would catch the 8 o'clock train."

No.

He should catch the 8 o'clock train so that he won't be late for the 9 o'clock meeting.

"He got up early so that he would catch the train that leaves at 8 o'clock." => Is this sentence still incorrect?

"I set the alarm clock for 6 am so that I wouldn't miss the bus." => The sentence on the same grammatical basis, is it also not correct?

AlpheccaStars"He woke up early so that he should/would catch the 8 o'clock train."
No.
He should catch the 8 o'clock train so that he won't be late for the 9 o'clock meeting.

Still no. You've changed the tense and added irrelevant information to the sentence.

Marold"He got up early so that he would catch the train that leaves at

Thank you very much, AlpheccaStars.