Do clotting factors tpa and pai-1 lead to degenerative osteoarthritis in the same way that lupus anticoagulant and prothrombin might? Is one of these pathways particularly detrimental during formation of osteoarthritis or avascular necrosis (if these factors are inhibited or modified in some way)?
First of all we should distinguish between the physiological clotting factors that are parts of the normal clotting pathways, and those that might affect clotting pathways but are not observed under healthy conditions.
TPA (tissue plasminogen activation), PAI-1 (plasminogen activator inhibitor) and prothrombin are normal clotting factors that are essential for blood clotting. Any deficiency (congenital or acquired) might cause certain pathologic conditions, including the osteoarthritis and avascular bone necrosis.
Lupus anticoagulant, however, is an antibody against cell membrane that is common for Lupus. This antibody can intervene into the process of clotting and increase the prothrombine time (the common lab method to test blood clotting properties), hence the name "anticoagulant". But this effect is just a sort of "side-effect" of this antibody, that leads to certain symptoms in case of auto-immune attack against different target organs.
So, after this introduction I can rephrase your first question as: "Does the deficiency of clotting factors TPA and PAI-1 lead to degenerative arthritis in the same way that lupus anticoagulant and prothrombin deficiency might?"
The part of the answer is already in this question: yes, the deficiency of these factors might and under certain conditions, leads to the development of osteoarhritis and avascular necrosis.
I must confess, I found no evidence whether the underlying mechanism is different or not. Papers just prove that these factors are discovered in the affected joins, and see the correlation in mice models between the factors and the articifially induced arthritis. But I found no study which would try to address the mechanisms of these actions or to show, whether these are different.