While these practical considerations are interesting, I think there is another observation worth making as well.
If you really can be fired without cause or notice and at the loss of most/all of your interest in the business, you have no cards and anything you do is a bluff.
If you really are dealing with cofounders who are are willing to push you out of 40% of your interests without offering much of anything in return as soon as the going gets good, then you have no reason to trust they won't push you out of the remaining 60% the day before any lock-up expires.
In that case, your best options may be either to lever the practical value that keeping you on board has right now to get a better, more secure deal immediately -- one where you won't be vulnerable to being kicked out arbitrarily and without proper compensation in the future -- or to assume you're going to get screwed when your lock-up ends and leave now.
It's a good idea to negotiate at this point rather than caving to the (probably very bad) deal being offered as an opening gambit by the cofounders, but the bottom line is that if they can fire you whenever they feel like it and you have no airtight contractual right to compensation if they do, nothing else you negotiate now actually has any value at all.
(Edit: Obviously if you opt for the "apply leverage" option then you do it nicely. I'm not talking about lawyers-at-dawn and threatening to walk if they don't meet your every outrageous demand or anything silly and confrontational like that. But I think it would be perfectly reasonable to expect solid guarantees that your remaining interests will retain meaningful value in exchange for whatever you are willing to give up here, such as accelerated vesting and a condition that if they let you go early then there's something in it for you.)