The only time I ever 'planned' were in SACs. In the exam I pretty much just scrawled down my three main ideas in key words just so I didn't forget them later on. So, I'm not a very 'planny' person. Thinking quickly was one of my best skills re: English.
One thing that I remember finding very helpful in the SACs though, was to write out my three topic sentences, word for word. For me, the most I would ever hesitate was when I was writing my topic sentences/starting off a paragraph, so by doing it all in one during planning time, my actual essay went ahead like a steam train because there was no more hesitation. Doing this also wrote half of my introduction for me, because I put my main ideas in the intro, so by writing out my main ideas I just had to change it up in the intro. Two birds with one stone! Then I jotted down some really good evidence in case I would forget. For my one and only time of planning an essay, each paragraph would have looked something like this --
-Rose utilises 10th Juror as an embodiment of 1950s McCarthyism in its entirety, condemning the xenophobic and prejudicial behaviour that manifests as a result.
-They hate... destroy us
-them. they. exclusive
-weather?
-cold?
-masculinity?
-(something)
-(something)
So above, I've got my TS. I know I will use the evidence "They hate us... they want to destroy us!" and analyse that. I also know I will be analysing the way in which 10th Juror's use of exclusive language "them", "they", (and perhaps even 8th Juror's "She's one of 'them' too, isn't she?") demonstrates xenophobia. The next three points are just there as triggers during the essay. I would have no idea if I were going to write on the weather, his cold, or masculinity, they're just there to prompt me making a decision in the middle of the paragraph. The other two somethings is evidence I would have jotted down but can't remember anymore.
You can see I'm a bit of a chaotic person/planner.
Probably a little bit far from what you'd personally like to do, but thats just my $0.02
You say you run out of time because your plan is not detailed enough -- you could try not being very detailed at all and just letting your writing flow from your mind... but this won't work for everyone. Lol. Happy writings!