> Next time, consider having a buy-sell agreement, vesting, options rather than shares, etc. irrespective of which side of the transaction you are on.

Huh? Based on the situation described by the OP, it sounds like he or she owns shares outright, possibly free of any major restrictions. This is the very best scenario a (former) employee will ever be in because the company has far less leverage.

Buy-sell agreements, vesting and options almost always work against the interests of employees and former employees.

Perhaps the OP will be on the other side, next time. Perhaps the OP overpaid for their shares this time. Perhaps a buy-sell agreement would have established a higher valuation or simplified the current transaction by injecting obligations and certainty. Energy that goes into buying the shares back is mostly a distraction and makes the company less likely to succeed and thus the shares may be worth less.

Suppose the OP holds out until the offer is quadruple. It's only the difference between a weekend in wine country and a week in Barcelona.

sweat equity = no money invested. At the moment I think I'm planning to hold out unless he's willing to pay for a third party evaluation.

Appraisals are made for a purpose. The person paying has more influence on that purpose. If the offer does not interest you "no" is best. If you want to move on, sell.