A no dilution privilege is precisely that, a privilege and not a duty. There is no reason to believe the shareholder is being greedy, after all, they are adding risk to their own position at the same time. A no dilution privilege only gives the right to maintain a constant percentage, if there are no resources to protect or maintain that right then it vanishes as if it did not exist.
"Full consensus" is not a well-defined term. Hopefully, the articles of incorporation define what that means exactly or it will simply be a majority-rule based decision.
Unless he is the majority shareholder and controls the board, then he cannot force the shareholders to dilute. If he is the majority shareholder, then it was foolish to enter into a written contract regarding the firm when informal understandings and ideas mean nothing legally. If you believed you were going to be protected, but are not, then the lesson is to hire a good attorney to explain fully the set of scenarios that could happen in the future.
Things like this are very common with angel investments and venture capital investments. Indeed, they plan for it. If they insisted on the no dilution agreement, now you know why.
The only control you could have is to get a majority of the existing shareholders to refuse to expand the company and to choose a board that will support your interests.
I realized that I didn't fully answer the question. The only real choice is to borrow money. Class B Common Shares have to get voting rights or they are not common shares. Preferred stock won't work here unless someone is very generous. Preferred stock is a creature of the tax code and unless one of the partners or a vendor is a corporation, nobody is going to want it. Debt issuance is your only escape from dilution if every partner cannot pony up their proportionate share of the needed funds.
You will want to visit a local attorney to see how the local judges would interpret "full consensus." Governance structures in corporations are important as is the language people put in charters and by-laws. Contingencies like this should be mapped out before capital formation and not after founding. A board of directors has a fiduciary duty to the shareholders and the firm. The language may be interpreted with respect to that duty if the issue is survival rather than expansion.
In the case of survival, a judge may reject an individual shareholder's veto if it kills the value to all shareholders. If it is about expansion, the judge may simply say "too bad." This is a question for a local attorney first and foremost. The judges in your county or parish may react differently than a judge in a neighboring county or state. There could also be decided law on this matter in your jurisdiction.