Coverage begins on the date that coverage would otherwise have been lost by
reason of a qualifying event and can end when:
 a.. The last day of maximum coverage is reached
 b.. Premiums are not paid on a timely basis
 c.. The employer ceases to maintain any group health plan
 d.. Coverage is obtained with another employer group health plan that does
not contain any exclusion or limitation with respect to any pre-existing
condition of such beneficiary
 e.. A beneficiary is entitled to Medicare benefits

Trust me insurance companies share information, they will know you have
Medicare. Medicare has very limited drug coverage. Can you qualify for a
Medicare  HMO Plan through Kaiser ? They make have limited enrollment times.
Also Medicare HMO I believe you are limited to one change per year so be
careful you maybe stuck with the plan for a year.