If you were going to take Classic Traveller, Books 1-3 and rewrite them to fit more modern rules layout, what parts would you clarify, what parts would you bring in from Books 4+ into the core rules, what tweaks would you make that still maintain the flavor of CT?
You just pretty much described my house rules.
I have re-created LBB 1, 2 & 3 for my rules.
I include Supp 4 and B1 characters. I do the 2 skills per term.
Combat is pretty close but armor stops damage.
At first I borrowed a lot from MGT starship design as I was very fond of the G/hour thing but I found I was doing all the math and my players didn't care (caveat been a number of years since I played Traveller). So I decided to just keep Book2 pretty much as is.
But what Book 2 was missing is a variant on weapon types (i.e. rail-gun, torpedoes, etc.). I like the old world Asimov style of SF that CT seems to give me the feel for so I wanted to keep a lot of that and not over-do the weapon selection.
But the ship design could use with some more 'stuff' (i.e. sickbay, mess, etc.).
I added skill progression (roll box cars get a check on that skill, +1 check than skill level get a level boost) -- learning a skill or studying to improve is 2 years study for each +1 skill.
I have my own house rules Psionics that I don't always use (Psi is fantasy so why have magic in a game of hard science?)
Other than that, I keep to the books as is.