Credit Card Processing for Monthly Recurring Billing

We have used the same vendor for ten years and we are sick of him. He has never really helped us understand the industry,  how things work, or helped us with improving operations. Service is intermittent. Problems are frequent. There are three areas that we ought to be able to really improve our situation.

1. Declines processing.  On any day, X% of our monthly subscribers are declined.  They are declined conceptually for a few reasons:
A.  insufficient funds
B.  expired credit card
C.  updated credit card due to security
D.  credit card account closed

Our vendors returns a few different pieces of information on the credit card declines:
1.  Call a 1 800 number to get the sale approved. The number is our own credit card processor who then gives us a phone number and the credit card number so that we can get a voice authorization. This is time consuming and results nine times out of ten in a failure.
2.  Invalid account number. Does this cover B, C, & D?
3.  Expired.
4.  Declined. This is the vast majority but they do come with a code: 0700540009  (BTW, if you google that code you get a fair number of people asking about what that decline code means).

Our traditional system of handling declines is to try again every ten days:
D1 - The first decline. We ignore it.
D2 - Second decline. If they are an active user, we send them an email
D3 - Third decline. If they are an active user, we send them an email and turn off their account with a message
D4 - If they are an active user, we send them an email and turn off their account with a message.
Also, we notify those with credit cards that are going to decline in the next 60 days that they need to update their credit card.
Recently, we've tried some robocalling to notify our users about declines and that has been surprisingly successful.  No numbers yet. We used to try to call ourselves and never found a way for it to be effective.

Questions - Ideally by A, B, C, & D above...
1.  Overall percent of D1s of billings?
2.  Overall number of D1s that become D2s?
3.  Overall number of D2s that become D3s?
4.  Overall number of D3s that become D4s?
5.   Credit card updates by users because we notify them that their credit card is expiring?
6.  Percent of each type of decline that our vendor returns to us?
7.  Updates between D2/D3, D3/D4?

Overall, our real questions are:
- What's the best method for avoiding declines with updaters and submission of AVS data and whatever.
- Once declined, how best to proceed in terms of trying again, contacting user, using technology to update?
BTW, all of this is focused on recurring billing cancellation, what about initial cancellations?

2. Costs. We are still in a system of tiered pricing which is confusing. There are costs and credits. Overall, we are paying ~4% to the gateway, processor, and credit card vendors. A lot!  Just getting this down by a percent will save us a lot of money per year.

3.  Reliability and reports. Compliance too.