>>strike 3 at least.
>>let them pay for the duration of the fourth clause - penalty 3 to 10 times the sum agreed upon if you decide otherwise.
>
>My lawyer says it's too ambiguous, so I'm going to try to convince them to use my standard contract.

IMHO he has a point. But to show your willingness, you might tell them in another mail,
that you might consider 4 if specced to be reasonably clear, if they pay you
- it is an area of your work you are excluding from your income.
If just the standard contract is sent, some picky potential clients might be miffed.
Picky they sound already - but if you really want the deal,
show that you have tried to put yourself into their shoes and find a way for you to sign most of it.