Conditionals and modals in reported speech

Hi,
I asked about this stuff in another thread, but maybe the thread was confusing, I got no replies. So I decided to post the senteces I wrote in another thread, this. Basically, I need some opinions on this:

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Many people say that "could, should, might, would" don't change in reported speech. I don't think so, but let's see:
I'd like to go to Jenny's party ----> He said he would like to go to Jenny's party (I would say this is ok only if Jenny hasn't had the party yet)
I'd like to go to Jenny's party ----> He said he would have liked to go to Jenny's party (I would say so if Jenny has already had the party or she's having the party now)
You should eat more vegetables -----> My doctor said I should eat more vegetables (I'd say this is ok as a general statement, I should eat more vegetables, that's good for my health)
You should eat more vegetables in the next few days, until you get well -----> (After a month) -- My doctor said I should have eaten more vegetables in the next few days, until I got well (I wouldn't just say "should" here. That's a past situation, I don't need to eat more vegetables now)
If you catch that disease, you could even die -------> They told my grandfather that if he caught that disease, he could have died (I'd say this is ok if my grandpa has already died, or if there's no possibility of dying or catching that disease now)
If you caught that disease, you could even die ------> They told my grandfather that if he had caught that disease, he could have died (Same as above, that is, I'd say this is ok if my grandpa has already died, or if there's no possibility of dying or catching that disease now)

I could go on, but I think you will have understood what I mean by now. I left out "might" from my examples, I think it's a little different, since "may" has practically the same meaning in many contexts. So "might" can often be seen as the past of "may", and we don't need to backshift it to "might have". By the way, the same is true of "could", we can sometimes see it as the past of "can".

As for "conditional sentences", my little example is:
If I had the money, I would give it to you -----> He said that if he had the money, he would give it to me (This way, I think what he said is still true)
If I had some money with me, I would pay you a beer -----> He said that if he'd had some money with him, he would have paid me a beer (Past situation, I would have paid me a beer on that occasion, this is not a general statement as the above one)
If I had enough money, I'd move straight to the US! ------> Hey, did you know Bill is in the US now? - Ah, he made it then! Actually, I remember he once told me that if he'd had enough money, he would have moved straight to the US. (no personal comments, there's enough context)

End of the story guys, it took some time but I finally managed to invent some examples the way I wanted. I know this post is long, sorry, anyway I just need some opinions on what I wrote, nothing more. That's just my opinion on the sentences, and I'm not sure of what I think at all!
Thank you in advance.

Hi there Koyeen,

Comments on two of your sentences...

You should eat more vegetables in the next few days, until you get well -----> My doctor said I should have eaten more vegetables in the next few days, until I got well

 I don't think it's appropriate for the situation. The context has a  future meaning whereas ''I should have eaten'' has a past one. 

 ''I should eat more veggies in the following days''.

If you catch that disease, you could even die -------> They told my grandfather that if he caught that disease, he could have died .

 ''If he caught that disease, he could even die.''  There still is a risk.

 

If you caught that disease, you could even die ------> They told my grandfather that if he had caught that disease, he could have died

 

'' If he had caught that disease, he could have died''  but he didn't, your grandpa is fine now.

 

  Hope they are correct..