Workers compensation only applies when the illness or injury can be confirmed as having been caused by your employment.
MA does not have a state disability plan.
Since unemployment and a private employer's disability plan are incompatible with one another (if you are eligible for one it's about 99% certain you are not eligible for the other) the fact that you received unemployment means you almost certainly were not receiving disability benefits from your employer.
The above translates to No, there is no way to bridge the six years with an employer plan.
If I am wrong and you are part of the 1% who somehow managed to collect both unemployment and LTD benefits at the same time (something I've never heard of in over 40 years of working in employee benefits, but I cannot ABSOLUTELY state has never happened) by all means let us know.