The last thing you want is for the insurance to accidentally lapse for nonpayment and not have any coverage....for either party.

My main question is if I need to have/should ask them to sign another year long lease or let it lapse into month to month.

Not only do you get copies of the policy declaration pages, you will receive renewal notices, notices of cancellation(either through cancellation or lapse), and as additional interest, can inquire at any time whether policy is current without going through the tenant.

Ultimately though an entire week went by with no one finding out any answers and just letting COE lapse?

It can be very difficult to evict a tenant for lapse of time and for any other reason other than non payment.

So, will the lapse in time disqualify me from providing proof of two years working if I were to lets just say, apply one year from now?

It stinks when sometimes the first few deals are the bulk of the 10 flops you're going to have, but if you keep your huge, long-term goals in mind, it makes the individual and momentary losses more manageable and even expected!

(one time deal, not every year) They also charge more for an insurance policy if the property hasn't been continuously insured. ie, insurance lapsed between the time we bought and insured the property and we got socked for that.

If you have a lapses in time in landscapers you will have rodents again.

Due to their early departure, for which I was not really prepared, and the extensive damages, that period has just lapsed.