With my intent to paint alla prima using Liquin Original medium with oil paint on Ampersand Gessobord, are there any problems combining OMS with Liquin Original and including an oil color to seal the India ink and tone the panel?
That should be fine as long as the ink is not applied so thickly that it is a glossy coating. Honestly, I would use water soluble ink rather than shellac-based waterproof ink. Either would likely work fine. Make use that you are not using a dye-based ink but rather one with carbon black as the coloring component. There may be some bleed with dye-based inks as some of the dyes can be sensitive to organic solvents AND, many of them are not lightfast.
Thinking about it more, make sure that the gessoboard is absorbent enough to take the ink well. Inks are so fluid that I would want to make sure that the ink did not bead up. Likely this would be fine. If it turns out that the ink does bead, I would just switch to the Clayboard from the same company (not because of brand supremacy, nor against it, but because you appear to already have justified faith in the company).
If you go the Clayboard route, you may want to cut the absorbency of the panel after the ink stage but before the proper oil painting stage. In the past, I have isolated the underdrawing and lessened the absorbency of such a panel using a thin judiciously applied alkyd medium rubbed on using a rag in a circular motion. This should be continued until there is no visible medium on the surface and it appears satin. In a way, this is a modern adaption of the oil based imprimaturas of the Renaissance (although those were usually, but not always, pigmented. However, you mention toned so, perhaps, you intend to apply a pigmented coating anyway.
I hesitated to mention the above procedure as it is very easy to overdo it an create an overly slick surface; but if properly done, the results are superior to applying shellac or a spirit varnish since the isolation layer would be insoluble in the solvents normally used in painting and even conservation.
An additional precaution is that this methods should not be used if one plans on leaving any part of the panel uncovered by opaque or at least semi opaque paint. Even though alkyd mediums do not yellow as bad as some media, they do yellow and one would not want this to remain exposed to discolor over time.
