Exceptional coordinatizable MOLs without orthogonal large partial frames

Let $L$ be a modular ortholattice. It is subdirectly irreducible if it has a least nonzero congruence, and it is coordinatizable if it arises from the lattice of principal right ideals of a suitable regular $*$-regular ring. An orthogonal large partial $n$-frame is a family satisfying

$$\sum_{i=1}^m a_i=1,\qquad a_i\sim a_1\text{ for }i\leq n,\qquad a_i\sim y_i\leq a_1\text{ for }n<i\leq m,$$

with $m\geq n\geq 3$ and pairwise orthogonal $a_i$.

Exceptional-frame conjecture. There are subdirectly irreducible coordinatizable MOLs of height at least $3$ not containing an orthogonal large partial $n$-frame.

The claim is presented as a conjecture in the discussion of whether orthogonal large partial frames characterize coordinatizability. Its status is not resolved in the source.