sclerotherapy ineffective thus far despite four treatments with proper aftercare and certified cosmetic dermatologist

If the venous insufficiency is not treated, sclerotherapy results may be marginal at best or if they are successful, reticular and spider veins are at high risk of recurrence. It is not only important to check for truncal venous insufficiency but also look for and treat perforator venous insufficiency. The spider veins are the 'tip of the iceberg' as there is much much more disease below the skin - so treating the spider vein is only part of the treatment. The feeder veins, the perforator veins have to be treated for a successful outcome. This is an expensive endeavor in terms of time, resources, catheters, experience and money spent. 

I agree that you should have a full venous evaluation with a venous reflux ultrasound.  Sclerotherapy is a process and can take anywhere from 2 to 10 treatments to have results.  However, after 4 treatments, there should be some noticeable improvement.  If there isn't, then I would be suspicious that you may have underlying saphenous valvular reflux contributing to the failure of the veins to resolve.  Think of your veins like a tree.  Sclerotherapy is treating the branches, but if the problem  is in the trunk, the branches will not get better.

I have some patients who have needed 10 or more sclerotherapy treatments because they had so many reticular veins. Others may need 2. It's hard to comment on this specifically, but it's pretty much impossible to not have results from sclerotherapy. As the vein is being injected, it goes away and blanches. Then it absorbs and goes away over time. So you can pretty much tell right away that you are getting results for a patient. Most patients who have big vericose veins and vascular sites also need sclerotherapy for the smaller veins too. That's pretty common.