The small signal diagram would be the same just with polarities reversed, so you can write it as \$I = g_mV_{sg}\$. As long as you aware of polarities though, either way could be used.
Here and here are reasonable documents with PMOS (and NMOS) small signal models and related equations (see first link, 8th page for diagram of both together)
The usual practice in teaching MOSFETs is to make all the derivations for NMOS and say something like: "for PMOS it is very similar, just switch the nodes...". Then it takes a whole lot of time to understand the actual difference between PMOS and NMOS.
I tend to believe that this is your case: you do know how to solve problems with NMOSs, but you do not have much experience with PMOSs.
First of all, the transistor in the schematic seems to be wired incorrectly (as pointed out in one of the comments).
Secondly, the current equation for PMOS in saturation is:
$$I_{SD}=K \times \frac{W}{L} \times (V_{SG}-|V_T|)^2$$
Substituting:
$$I_{SD}=250 \times 10^{-6} \times (V_S-0.714-1)^2$$
(note that \$V_G=0.714V\$ according to my calculations).
The current should also satisfy:
$$I_{SD}= \frac{5-V_S}{1200}$$
Equating the above two and solving for \$V_S\$ yields:
$$V_S=3.75V$$
We must also check that saturation condition holds (in order to justify our a-priory assumption):
$$V_{SG}=V_S-V_G=3.75-0.714=3.036V>|V_T|$$
and
$$V_{SD}=V_S-V_D=3.75-(-5+4000\times I_{SD})=4.59V>V_{SG}-|V_T|$$
Both conditions hold therefore PMOS is conducting and in saturation.
I suppose you might have been using a more sophisticated MOSFET model for Spice simulation, therefore the answer you got there is different (although pretty close).
Best Answer
The only real difference is in the mobility of the carriers, where electrons are faster than holes (around 2x) thus giving nMOS transistor a 2 times better performance for everything else equal.
About notation, it's mostly a practical thing, and the small signal model is an abstraction that you make to analyze a circuit. So you can use it the way you understand it better.
For instance, I usually use magnitudes (flipping notations drives me crazy) and then determine the direction of the current and voltage from the circuit. So the nMOS will generally have a current from drain to source, and the pMOS from source to drain, both with positive sign.
pMOS's \$I_{SD} \$ will be proportional to \$V_{SG} - |V_T| \$, where nMOS's \$I_{DS} \$ will be proportional to \$V_{GS} - |V_T| \$. Note that for the pMOS, you can flip
SGandSDand still obtain the right values, as long as you use the absolute value of Vt.