Has any Buddhist meditator claimed that the mano-vijnana has a base to differentiate it from the other consciousnesses? Has any Buddhist meditator claimed that the mano-vijnana has a base (I don't mean that in any technical sense) to differentiate it from the other consciousnesses?

If so, what is it called, and when is its action suspended?
According to the Theravada Abhidhamma Mental Consciousness (mano-vijnana) is heart based. This is what Buddha realised through his meditation. Other consciousness arise with the respective faculties and the base, e.g. eye-consciousness with the eye.

It is suspended when you are in Nirodha Samapathi and in Bavanga consciousness. Also perhaps in Pala Samanapathi if this result in a momentarily entering Nirodha Samapathi but not very sure on this as there are different view on this.