When you buy a pre-cut set of matched top material for a LP they want to sell you 1/4 or 3/8 in stock. The old les Pauls started with a 7/8 in top and they carved it down.That was 1x material back than 5/4 was 1.1/8
If you are looking at 1/4 or 3/8 then you are looking in the wrong area.....these are for droptops. And nobody selling to make a carved LP will sell that, or buying for a LP will buy that.
1 1/2 to 1 3/4 is typical bookmatched maple stock for someone who resaws themselves.
3/4 to 7/8 pair is typical luthier wood for someone who has access to thicknessing/planing.
Now you're getting into making, I'm sure you'll start to learn what
actually goes on with the mechanics of a carved top, rather than some of the slightly off assumptions you have so far.
#1 5/8 is a typical maple thickness. This has been measure by people who have gone over many bursts with a fine tooth comb. If you want the details, then Bartlett Woodworking plans has a generic 59 plan where every detail and possible measurement you could hope for is there. In this plan the outline is smoothed by using many different guitars to remove some of the hand sanding idiosyncrasies and get closer to what the initial cut shape would have been. There is a 'precise' plan with the very outline and dimension of 1 burst from 1959 should you want that.
You can recarve plenty fine enough from a modern carve if you actually know about the contours. Its the recurve that the modern non-historics miss......but as they leave MORE wood than with the recarve you have room to move. As to the old or historic guitars - well if you see a historic that doesn't match a given vintage guitar, who is to say it doesn't match another one??? They are snowflakes....as you should know if you are up on vintage guitars.
#2 Re-tops are done often for cosmetics - a 'better' flamed top. Or in some vintage guitars one that is centre seam bookmatched if we are talking goldtop conversions.
#3 It matters not what you use to carve the wood with - its great you want to do it by hand, but sawdust is still sawdust whether you use a machine or a hand tool to do it.
#4 Bridge height is complicated. On a LP it is a combination of maple top thickness, rim or edge height, neck plane angle and pickup plane angle plus the specifics of the carve. And these interact with each other of course. Having made quite a few burst clones from scratch as well as other shaped carve top guitars you cannot place the height only to one aspect.
And because every guitar was hand sanded the precise neck angles vary. So just saying 'old guitars had lower bridges' is quite wrong.
What you need to do is go over to the Luthiers Corner section. There you can start to learn what goes into making a guitar. There is a current thread with videos called "Freddy's Build'. You can also delve into the archive for the Ex Nihilo Vintage Burst Build and the Bartlett Build. As well as Preeb's (Gil Yaron) celebrated no-holds barred build on TDPRI