It doesn't sound to me like they clearly want the OP to sell. It actually sounds like the opposite. The OP wants to get out, and they responded with a lowball offer which, if anything, would motivate the OP not to sell.
No, they responded with a lowball offer because they feel the OP is motivated to sell at any price.
His best bet is simply not to sell and to wait for them to make an offer.
OP is confused about the shareholder and employee roles, they are not linked other than through vesting and the shareholder agreement (which they have presumably signed).
He can easily quit as an employee while remaining a shareholder in the company. Those roles need not be connected forever and there usually are - vesting excepted - penalty free ways of stepping out of a company while you keep whatever shares you already have. Clawbacks in a situation like that are very rare.
Where "what I'm owed" is quite vague, or has only recently increased as in the case of growth companies, 10 or 20% might actually be accepted, or at least interpreted as a good faith start to negotiations.
An offer of 1% is more obviously not the correct amount, and encourages people to lawyer up rather than counter offer (it screams "we're only offering this token amount because someone suggested our original plan of not giving you anything might not work")
