What the senior is refusing is the intercreditor agreement, not the $2.5m. A mezz loan obligates them to give a third party notice of every default, honor a standstill, accept cure payments from someone who isn't their borrower, and live with a purchase option and a UCC sale that can change control of their borrower without a mortgage foreclosure they control. That's a set of ongoing duties on their loan file. Preferred equity, structured the way most seniors want it, gives them a change of control remedy that lands inside the entity documents they already approved, with a pre-approved substitute manager and no separate agreement binding the senior's own hands. Whether their documents actually prohibit the pledge, and at what tier, is a document question, so have your counsel read the additional indebtedness and transfer covenants rather than taking the loan officer's summary.
On your economics, the pref at 13 with a hard redemption at month 48 is closer to debt than you're treating it. If it isn't redeemed, the typical remedy is control rights and a forced sale, which is a maturity with a different name. Price both against your refinancing window instead of against the coupon. $12m at 6.75 on a 30 year schedule runs roughly $933k a year, and $225k of current pay on the mezz version, the 9 of the 12 that pays in cash, puts you near $1.16m of cash debt service. Whatever your NOI is, run it at 1.15x and see which instrument survives a flat year.
One path seniors do say yes to: they hold the additional dollars themselves as a stretch first, or the gap capital comes in at a holding company above the pledgor with no lien or pledge touching the SPE at all. That second version costs more because the collateral is weaker. If the senior is a securitized loan, any consent runs through a servicer and can take a long time, so get their answer and their required form in writing before you spend money on documents.