Is this a "valid" CDMA modulation?
I think you are trying to mix orthogonality for $GF(2)$ and $R^n$. For the sequence $010101000001$, if station 2 had tried to demodulate it, he will have to take groups of 2 bits, multiple (AND) and add(XOR) them, to decode whether bit 0 or 1. Station 2 would have got all 0s because $10$ and $01$ is 'orthogonal' for station 1 and 2. So yes, #3 is indeed a valid CDMA scheme in $GF(2)$. I stress, it is a valid CDMA scheme only in $GF(2)$. It is not related to #1 and #2 (see below why).

Setups #1 and #2 are valid CDMA schemes in $R^n$ (real number vectors) because orthogonality is validated by $x_1^Tx_2$. For #2, you cannot validate orthogonality by dot product of vectors containing 0 and 1. Because for $W_4$, rows 3 and 4 are not orthogonal. So, $0$ has to be represented by $-1$. Even though logically we switch $0$ and $1$ as NOT operator while forming Walsh matrices, orthogonality is not valid in $GF(2)$.


  On the other hand, I cannot make setup #3 work with codes that resemble normal Walsh matrices


$[1,1;0,1]$ would not correspond to CDMA because whether in $GF(2)$ or $R^2$, they are not orthogonal. $[1,0,0,0;0,1,0,0;0,0,1,0;0,0,0,1]$ is orthogonal in $GF(2)$ as well as in $R^2$ which is same as your multiplexing in time but it is still technically a CDMA scheme (if you transmit each bit at 4x higher rate).