Rather, subjunctive clauses recruit the bare form of the verb which is also used in a variety of other constructions.
I thought I'd better tell my story before other people told it for me.
Basically the past in the past.
Mostly so in speaking, could also happen in writing depending on context and style.
This is because if a speaker offers two options for an activity, as in these examples, they are almost certainly in the same timeframe.
Also the aforementioned modal verbs could, might and should may replace would in order to express appropriate modality in addition to conditionality.