Sale, refinance, new debt, affiliate contracts and admission of new partners survive negotiation almost always. Those are event-level decisions with time to make them. The $50k capex approval and the 10% line item variance are where operators genuinely lose weeks, and what usually happens is the threshold moves up and gets a deemed-approval clock attached, five or ten business days, so silence is a yes. A 10% variance test on a single line item is close to meaningless anyway on a renovation budget, since line items move constantly while the total holds. Test the total contingency and the total hard cost instead, and require re-forecasting in writing when either moves past a set percentage.
Deadlock is a real objection. A buy-sell only functions if the party who triggers it can write the check, and your operator with $500k in cannot buy out $4M. Which means a buy-sell in your document is effectively your option to force a sale of his position at a formula price, and he'll fight it or agree to it and then be unmanageable.
The provision that does the work here isn't consent at all. It's the funding default remedy. If the project needs another $600k and he can't fund his 11%, what happens? A dilution formula at a penalty multiple, or a partner loan accruing at a punitive rate, gives you actual control at the moment control matters. Pair that with cause defined to include failure to fund and material deviation from the approved business plan, rather than fraud and gross negligence alone.
One thing to check before you fund. If he's the loan guarantor, your removal right is constrained by the lender documents no matter what your operating agreement says. And how much day to day control an equity partner takes can affect its own liability exposure depending on the state of formation, which is a question for your counsel rather than a drafting preference.