I went with Embrace Pet Insurance.
Experience Better Pet Insurance with EMBRACE
Thank god I have not had to use it. So I don't know about turn around time. They offer 800 fax number to fax all claims, and if you sign up for direct deposit they will deposit any reimbursement. I believe the advertised turn around time was 2 weeks. (I would think if you have a good relationship with your vet, in a time of need most should be willing to accept partial payment or wait the 2 weeks for reimbursement.) They do prefer to do the paperless thing. But can have mailed claims/checks. Totally up to the insured.
One other thing I thought was good, in cases of extensive treatments, while precert is not required, you can have a certification done from the standpoint of what Embrace will reimburse based on what the vet provides as treatment plan and cost. I think that's good so you know what to expect up front with claim reimbursement.
There is a "healthy pet" discount, where the deductible decreases by $50 for every year a claim is not filed, and yes it can go down to zero. If a claim is filed the deductible is honored for that year and then resets to the full deductible on the renewal, and discounts can be applied all over again.
Hope I never need it but now I have the peace of mind.