Hi Sophie,
I will often start dogs on herbs even while NSAIDS are in play, then when we see improvements, find the lowest required dose of the drugs. It's advantageous to reduce dose not only to mitigate adverse events, but also - as you say - to reduce the interference in the action of the herbs by the drug.
They are compatible for long term use, with each balancing the adverse effects of the other. NSAIDs avoid acute flare ups from too much blood entering the area. Blood tonics and movers help avoid GI ulcers and circulatory impoverishment that impedes healing and lesion resolution
As a visual for how you could use two contrary forces to advantage, think of driving a car. To move forward you rarely want to 'floor it', so a measured response is called for. Likewise, in an automatic transmission, you don't turn off the engine to stop. You apply gentle break pressure, even as the car remains in gear and continues to be driven forward. So, too, in our patients are we seeking the ideal balance of these two forces - ice pack and 'hot tub'
Steve