This is common phenomena being faced by candidates who quit jobs either to join other firms or to pursue other ventures. When this fails, land in job search and face such situations. My suggestions are-
Ensure the facts are clearly mentioned in your CV, timeline properly tied up and they are adequately verifiable. If possible one should produce enough convincing documents in support of the facts. Without documentary support like, letter heads, visiting card, business tie-ups had mentioning your name. A relieving letter from the existing business entity will add to your claims. Like wise you should mobilise the support of an existing employee of the prospective firm of fairly in a sr.position to recommend you is an added advantage. On the contrary, if you name sake advance this stand just to fill up gap, it won't work that way. Even if you escape by securing the offer, you get caught when BVC report is out, in case the report reveals otherwise. So give a try either thru' your past colleagues, friends in employment, though it might not be upto your expectations. In case, if you could prove that you are the candidate they are looking for, sure you won't fail in your attempts. Not all employer view this in the same manner.